Benchmark results
Generated by the benchmarks harness over PGLib-OPF v23.07. Regenerate with cargo run -p benchmarks --release -- --out <dir> and copy the snapshot here. The solves are deterministic; the numbers reproduce on the recorded toolchain.
Provenance
| tellegen | rustc | clarabel | faer | powerio | os/arch |
|---|---|---|---|---|---|
178da99 | 1.96.0 (ac68faa20 2026-05-25) | 0.11.1 | 0.24.4 | 0.7.1 | macos/aarch64 |
PGLib v23.07 (arXiv:1908.02788, CC BY 4.0). Command: ./target/release/pglib-bench --out target/pglib-bench-20260720 --book.
Coverage summary
198 (case, variant) rows.
| status | count |
|---|---|
| caveat | 50 |
| failed | 2 |
| skipped | 3 |
| solved | 143 |
Reproduction of PGLib
Corpus roll-up of the per-case marks in the table below. “Reproduced” is an objective match (DC within 1%) or, for the SOCWR relaxation, a valid lower bound whose gap matches the published SOC gap. “Consistent” is an acceptable non-exact agreement: a DC the baseline also reports infeasible, or a SOCWR lower bound with a looser gap. “Mismatch” is a differing objective or a lower-bound violation.
| formulation | reproduced | consistent | mismatch | with baseline |
|---|---|---|---|---|
| DC OPF | 148 | 45 | 0 | 193 |
| SOCWR (lower bound) | 183 | 6 | 0 | 189 |
OPF correctness vs PGLib BASELINE
tellegen’s objective against the published value, per formulation: the DC OPF ($/h, constant cost included) vs the published DC, and the SOCWR relaxation (a lower bound on AC) vs the published AC. Δgap is tellegen’s SOC gap minus the published SOC gap; near zero is the steelman result (same Jabr family). The reproduces column is DC·SOC: ✓ matches the published objective (DC within 1%), inf✓ infeasible consistent with the published inf., ✓lb a valid lower bound whose gap matches the published SOC, lb a valid bound with a looser gap, ✗ a mismatch (a converged but differing objective), — no baseline.
| case | var | buses | DC $/h | PGLib DC | SOCWR $/h | PGLib AC | Δgap | reproduces |
|---|---|---|---|---|---|---|---|---|
| case3_lmbd | api | 3 | 10444.4 | 10444.0 | 10194.9 | 11242.0 | -0.01 | ✓·✓lb |
| case3_lmbd | sad | 3 | 5856.0 | 5856.0 | 5736.2 | 5959.3 | -0.01 | ✓·✓lb |
| case3_lmbd | typ | 3 | 5695.9 | 5695.9 | 5736.2 | 5812.6 | -0.01 | ✓·✓lb |
| case5_pjm | api | 5 | 78025.2 | 78025.0 | 77571.4 | 78950.0 | -0.00 | ✓·✓lb |
| case5_pjm | sad | 5 | — | — | 25164.9 | 26109.0 | -0.00 | inf✓·✓lb |
| case5_pjm | typ | 5 | 17479.9 | 17480.0 | 14999.7 | 17552.0 | -0.01 | ✓·✓lb |
| case14_ieee | api | 14 | 4797.6 | 4797.6 | 5691.8 | 5999.4 | -0.00 | ✓·✓lb |
| case14_ieee | sad | 14 | — | — | 2179.2 | 2776.8 | -0.01 | inf✓·✓lb |
| case14_ieee | typ | 14 | 2051.5 | 2051.5 | 2175.7 | 2178.1 | -0.00 | ✓·✓lb |
| case24_ieee_rts | api | 24 | 148845.5 | 148850.0 | 149168.3 | 161220.0 | -0.00 | ✓·✓lb |
| case24_ieee_rts | sad | 24 | 78122.5 | 78122.0 | 69578.9 | 76918.0 | -0.01 | ✓·✓lb |
| case24_ieee_rts | typ | 24 | 61001.2 | 61001.0 | 63344.6 | 63352.0 | -0.01 | ✓·✓lb |
| case30_as | api | 30 | 3092.1 | 3092.1 | 2767.8 | 4996.2 | -0.01 | ✓·✓lb |
| case30_as | sad | 30 | — | — | 825.9 | 897.4 | 0.08 | inf✓·✓lb |
| case30_as | typ | 30 | 767.6 | 767.6 | 802.7 | 803.1 | -0.00 | ✓·✓lb |
| case30_ieee | api | 30 | 16145.1 | 16145.0 | 17057.8 | 18037.0 | -0.00 | ✓·✓lb |
| case30_ieee | sad | 30 | — | — | 7412.6 | 8208.5 | -0.00 | inf✓·✓lb |
| case30_ieee | typ | 30 | 7472.8 | 7472.8 | 6662.2 | 8208.5 | -0.00 | ✓·✓lb |
| case39_epri | api | 39 | 252754.6 | 252750.0 | 253130.4 | 256770.0 | -0.00 | ✓·✓lb |
| case39_epri | sad | 39 | 150669.9 | 150670.0 | 147360.5 | 148340.0 | -0.01 | ✓·✓lb |
| case39_epri | typ | 39 | 136889.7 | 136890.0 | 137654.1 | 138420.0 | -0.01 | ✓·✓lb |
| case57_ieee | api | 57 | 34081.1 | 34081.0 | 33271.6 | 36242.0 | -0.00 | ✓·✓lb |
| case57_ieee | sad | 57 | — | — | 38391.4 | 38663.0 | -0.01 | inf✓·✓lb |
| case57_ieee | typ | 57 | 34773.0 | 34773.0 | 37529.7 | 37589.0 | -0.00 | ✓·✓lb |
| case60_c | api | 60 | 176378.6 | 176380.0 | 181189.2 | 185000.0 | -0.01 | ✓·✓lb |
| case60_c | sad | 60 | — | — | 108485.3 | 113500.0 | 0.05 | inf✓·✓lb |
| case60_c | typ | 60 | 90700.1 | 90700.0 | 92637.0 | 92694.0 | -0.01 | ✓·✓lb |
| case73_ieee_rts | api | 73 | 472183.2 | 472180.0 | 488422.7 | 509850.0 | -0.01 | ✓·✓lb |
| case73_ieee_rts | sad | 73 | 232679.1 | 232680.0 | 212280.3 | 227600.0 | 0.00 | ✓·✓lb |
| case73_ieee_rts | typ | 73 | 183003.7 | 183000.0 | 189706.1 | 189760.0 | -0.01 | ✓·✓lb |
| case89_pegase | api | 89 | 118452.5 | 118630.0 | 113367.9 | 129570.0 | -0.01 | ✓·✓lb |
| case89_pegase | sad | 89 | — | — | 106491.2 | 107290.0 | 0.01 | inf✓·✓lb |
| case89_pegase | typ | 89 | 104919.0 | 105040.0 | 106480.8 | 107290.0 | 0.00 | ✓·✓lb |
| case118_ieee | api | 118 | 231291.9 | 231290.0 | 184303.2 | 249610.0 | -0.01 | ✓·✓lb |
| case118_ieee | sad | 118 | — | — | 96535.5 | 105160.0 | 0.03 | inf✓·✓lb |
| case118_ieee | typ | 118 | 93100.7 | 93101.0 | 96334.7 | 97214.0 | -0.01 | ✓·✓lb |
| case162_ieee_dtc | api | 162 | 111570.9 | 111570.0 | 115655.9 | 120880.0 | -0.01 | ✓·✓lb |
| case162_ieee_dtc | sad | 162 | 106287.8 | 106290.0 | 101655.6 | 108690.0 | -0.01 | ✓·✓lb |
| case162_ieee_dtc | typ | 162 | 101462.3 | 101460.0 | 101654.9 | 108080.0 | -0.01 | ✓·✓lb |
| case179_goc | api | 179 | 1813209.8 | 1813200.0 | 1727618.5 | 1883400.0 | 0.01 | ✓·✓lb |
| case179_goc | sad | 179 | — | — | 754005.8 | 762530.0 | -0.00 | inf✓·✓lb |
| case179_goc | typ | 179 | 751881.6 | 751880.0 | 753089.1 | 754270.0 | -0.00 | ✓·✓lb |
| case197_snem | api | 197 | 15689.7 | 15690.0 | 16203.0 | 16363.0 | -0.00 | ✓·✓lb |
| case197_snem | sad | 197 | — | — | 1.5 | 1.5 | 0.03 | inf✓·✓lb |
| case197_snem | typ | 197 | 1.5 | 1.5 | 1.5 | 1.5 | 0.02 | ✓·✓lb |
| case200_activ | api | 200 | 40129.8 | 40130.0 | 40692.9 | 40700.0 | -0.00 | ✓·✓lb |
| case200_activ | sad | 200 | — | — | 27556.6 | 27558.0 | -0.01 | inf✓·✓lb |
| case200_activ | typ | 200 | 27479.6 | 27480.0 | 27556.6 | 27558.0 | -0.01 | ✓·✓lb |
| case240_pserc | api | 240 | 4624856.0 | 4624800.0 | 4636792.9 | 4692200.0 | 0.00 | ✓·✓lb |
| case240_pserc | sad | 240 | — | — | 3237213.7 | 3405400.0 | 0.01 | inf✓·✓lb |
| case240_pserc | typ | 240 | 3271442.2 | 3271400.0 | 3237193.6 | 3329700.0 | -0.00 | ✓·✓lb |
| case300_ieee | api | 300 | 659786.2 | 659840.0 | 679566.9 | 686040.0 | -0.01 | ✓·✓lb |
| case300_ieee | sad | 300 | 527243.9 | 527290.0 | 550597.4 | 565700.0 | 0.06 | ✓·✓lb |
| case300_ieee | typ | 300 | 517802.2 | 517850.0 | 550393.8 | 565220.0 | -0.01 | ✓·✓lb |
| case500_goc | api | 500 | 646871.6 | 646870.0 | 663185.9 | 688290.0 | -0.00 | ✓·✓lb |
| case500_goc | sad | 500 | — | — | 454907.9 | 487400.0 | -0.00 | inf✓·✓lb |
| case500_goc | typ | 500 | 440548.6 | 440550.0 | 453838.5 | 454950.0 | -0.01 | ✓·✓lb |
| case588_sdet | api | 588 | 392953.8 | 392950.0 | 387619.1 | 398760.0 | -0.01 | ✓·✓lb |
| case588_sdet | sad | 588 | — | — | 307081.1 | 329360.0 | 0.09 | inf✓·✓lb |
| case588_sdet | typ | 588 | 310125.6 | 310130.0 | 306447.9 | 313140.0 | -0.00 | ✓·✓lb |
| case793_goc | api | 793 | 372180.2 | 372180.0 | 321148.8 | 379800.0 | -0.01 | ✓·✓lb |
| case793_goc | sad | 793 | — | — | 263030.4 | 285800.0 | -0.00 | inf✓·✓lb |
| case793_goc | typ | 793 | 258308.0 | 258310.0 | 256757.9 | 260200.0 | -0.01 | ✓·✓lb |
| case1354_pegase | api | 1354 | 1558525.9 | 1558500.0 | 1578360.1 | 1608200.0 | 0.01 | ✓·✓lb |
| case1354_pegase | sad | 1354 | — | — | 1236022.1 | 1258800.0 | 0.24 | inf✓·✓lb |
| case1354_pegase | typ | 1354 | 1218182.9 | 1218200.0 | 1235968.2 | 1258800.0 | 0.24 | ✓·✓lb |
| case1803_snem | api | 1803 | 62064.2 | 61723.0 | 46102.3 | 80240.0 | 1.70 | ✓·lb |
| case1803_snem | sad | 1803 | — | — | 91290.5 | 106340.0 | 0.16 | inf✓·✓lb |
| case1803_snem | typ | 1803 | 87706.8 | 87696.0 | 90240.4 | 98335.0 | 0.20 | ✓·✓lb |
| case1888_rte | api | 1888 | 1961569.9 | 1961600.0 | 2013300.1 | 2019700.0 | -0.00 | ✓·✓lb |
| case1888_rte | sad | 1888 | 1353179.3 | 1353200.0 | 1373847.5 | 1413900.0 | 0.01 | ✓·✓lb |
| case1888_rte | typ | 1888 | 1352872.6 | 1352900.0 | 1373847.4 | 1402500.0 | -0.01 | ✓·✓lb |
| case1951_rte | api | 1951 | 2411505.2 | 2411500.0 | 2478404.2 | 2490300.0 | -0.00 | ✓·✓lb |
| case1951_rte | sad | 1951 | — | — | 2082719.5 | 2092400.0 | 0.00 | inf✓·✓lb |
| case1951_rte | typ | 1951 | 2031629.3 | 2031600.0 | 2082711.6 | 2085600.0 | -0.00 | ✓·✓lb |
| case2000_goc | api | 2000 | 1409993.7 | 1410000.0 | 1441231.6 | 1483900.0 | 0.01 | ✓·✓lb |
| case2000_goc | sad | 2000 | — | — | 977751.3 | 992880.0 | 0.00 | inf✓·✓lb |
| case2000_goc | typ | 2000 | 943042.6 | 943040.0 | 970446.9 | 973430.0 | -0.00 | ✓·✓lb |
| case2312_goc | api | 2312 | 615216.3 | 615220.0 | 546946.8 | 663440.0 | 0.03 | ✓·✓lb |
| case2312_goc | sad | 2312 | — | — | 444178.0 | 462350.0 | 0.00 | inf✓·✓lb |
| case2312_goc | typ | 2312 | 440328.5 | 440330.0 | 432953.7 | 441330.0 | -0.00 | ✓·✓lb |
| case2383wp_k | api | 2383 | 279125.8 | 279130.0 | 279125.8 | 279130.0 | -0.01 | ✓·✓lb |
| case2383wp_k | sad | 2383 | — | — | 1856608.1 | 1911200.0 | -0.00 | inf✓·✓lb |
| case2383wp_k | typ | 2383 | 1804090.4 | 1804100.0 | 1848908.7 | 1868200.0 | -0.01 | ✓·✓lb |
| case2736sp_k | api | 2736 | 977821.5 | 977820.0 | 939178.2 | 1017800.0 | -0.01 | ✓·✓lb |
| case2736sp_k | sad | 2736 | — | — | 1305707.8 | 1326600.0 | -0.01 | inf✓·✓lb |
| case2736sp_k | typ | 2736 | 1276033.7 | 1276000.0 | 1303994.5 | 1308000.0 | -0.00 | ✓·✓lb |
| case2737sop_k | api | 2737 | 755318.3 | 755320.0 | 733986.1 | 788310.0 | -0.01 | ✓·✓lb |
| case2737sop_k | sad | 2737 | — | — | 776126.6 | 790950.0 | -0.01 | inf✓·✓lb |
| case2737sop_k | typ | 2737 | 764009.8 | 764010.0 | 775689.9 | 777730.0 | -0.01 | ✓·✓lb |
| case2742_goc | api | 2742 | 505399.5 | 505400.0 | 471741.7 | 609960.0 | -0.01 | ✓·✓lb |
| case2742_goc | sad | 2742 | 259696.6 | 259700.0 | 271971.8 | 275710.0 | -0.00 | ✓·✓lb |
| case2742_goc | typ | 2742 | 259696.6 | 259700.0 | 271999.6 | 275710.0 | -0.00 | ✓·✓lb |
| case2746wop_k | api | 2746 | 531726.6 | 531550.0 | 511658.6 | 550480.0 | -0.01 | ✓·✓lb |
| case2746wop_k | sad | 2746 | — | — | 1205170.1 | 1233700.0 | -0.01 | inf✓·✓lb |
| case2746wop_k | typ | 2746 | 1178363.8 | 1178200.0 | 1203861.3 | 1208300.0 | -0.00 | ✓·✓lb |
| case2746wp_k | api | 2746 | 581827.9 | 581830.0 | 581825.1 | 581830.0 | -0.01 | ✓·✓lb |
| case2746wp_k | sad | 2746 | — | — | 1630588.4 | 1666900.0 | -0.01 | inf✓·✓lb |
| case2746wp_k | typ | 2746 | 1581425.1 | 1581400.0 | 1626493.5 | 1631700.0 | -0.01 | ✓·✓lb |
| case2848_rte | api | 2848 | 1488985.3 | 1489000.0 | 1527378.9 | 1531100.0 | -0.01 | ✓·✓lb |
| case2848_rte | sad | 2848 | — | — | 1285682.1 | 1289000.0 | 0.01 | inf✓·✓lb |
| case2848_rte | typ | 2848 | 1267732.3 | 1267700.0 | 1285034.3 | 1286600.0 | -0.01 | ✓·✓lb |
| case2853_sdet | api | 2853 | 2456065.6 | 2456100.0 | 2420923.4 | 2484300.0 | 0.01 | ✓·✓lb |
| case2853_sdet | sad | 2853 | — | — | 2033761.7 | 2069200.0 | 0.01 | inf✓·✓lb |
| case2853_sdet | typ | 2853 | 2036958.3 | 2037000.0 | 2033582.3 | 2052400.0 | 0.01 | ✓·✓lb |
| case2868_rte | api | 2868 | 2277460.8 | 2277500.0 | 2334871.0 | 2343900.0 | 0.01 | ✓·✓lb |
| case2868_rte | sad | 2868 | — | — | 2009425.4 | 2021300.0 | -0.00 | inf✓·✓lb |
| case2868_rte | typ | 2868 | 1966685.0 | 1966700.0 | 2007570.8 | 2009600.0 | 0.00 | ✓·✓lb |
| case2869_pegase | api | 2869 | 2966298.3 | 2966600.0 | 3026118.5 | 3063000.0 | 0.02 | ✓·✓lb |
| case2869_pegase | sad | 2869 | — | — | 2438499.1 | 2468700.0 | 0.10 | inf✓·✓lb |
| case2869_pegase | typ | 2869 | 2386115.8 | 2386400.0 | 2435400.7 | 2462800.0 | 0.10 | ✓·✓lb |
| case3012wp_k | api | 3012 | 851750.5 | 851750.0 | 728874.0 | 914590.0 | -0.00 | ✓·✓lb |
| case3012wp_k | sad | 3012 | — | — | 2578747.0 | 2619500.0 | -0.00 | inf✓·✓lb |
| case3012wp_k | typ | 3012 | 2509001.5 | 2509000.0 | 2574297.7 | 2600800.0 | -0.01 | ✓·✓lb |
| case3022_goc | api | 3022 | 666194.7 | 666190.0 | 594789.6 | 687360.0 | 0.02 | ✓·✓lb |
| case3022_goc | sad | 3022 | 599221.5 | 599220.0 | 584763.7 | 601430.0 | 0.00 | ✓·✓lb |
| case3022_goc | typ | 3022 | 599221.5 | 599220.0 | 584742.8 | 601380.0 | -0.00 | ✓·✓lb |
| case3120sp_k | api | 3120 | 1326454.4 | 1326500.0 | 1178608.6 | 1403500.0 | -0.01 | ✓·✓lb |
| case3120sp_k | sad | 3120 | — | — | 2141758.0 | 2174900.0 | 0.00 | inf✓·✓lb |
| case3120sp_k | typ | 3120 | 2087974.9 | 2088000.0 | 2135975.3 | 2148000.0 | -0.00 | ✓·✓lb |
| case3375wp_k | api | 3374 | 6272121.1 | 6272100.0 | 5865209.8 | 6364100.0 | -0.00 | ✓·✓lb |
| case3375wp_k | sad | 3374 | 7319637.3 | 7319600.0 | 7397595.4 | 7438200.0 | -0.00 | ✓·✓lb |
| case3375wp_k | typ | 3374 | 7317011.9 | 7317000.0 | 7397405.5 | 7438200.0 | -0.00 | ✓·✓lb |
| case3970_goc | api | 3970 | 1227776.4 | 1227800.0 | 1070893.9 | 1749400.0 | -0.00 | ✓·✓lb |
| case3970_goc | sad | 3970 | — | — | 958294.5 | 965550.0 | -0.01 | inf✓·✓lb |
| case3970_goc | typ | 3970 | 934219.4 | 934220.0 | 957739.2 | 960990.0 | -0.00 | ✓·✓lb |
| case4020_goc | api | 4020 | 1082422.1 | 1082400.0 | 1062324.8 | 1281700.0 | -0.00 | ✓·✓lb |
| case4020_goc | sad | 4020 | — | — | 812671.5 | 889690.0 | -0.00 | inf✓·✓lb |
| case4020_goc | typ | 4020 | 795061.9 | 795060.0 | 812181.5 | 822250.0 | -0.01 | ✓·✓lb |
| case4601_goc | api | 4601 | 796409.8 | 796410.0 | 687104.5 | 871240.0 | -0.01 | ✓·✓lb |
| case4601_goc | sad | 4601 | 1195553.7 | 1195500.0 | 822282.0 | 878180.0 | -0.00 | ✓·✓lb |
| case4601_goc | typ | 4601 | 793813.9 | 793810.0 | 821853.5 | 826240.0 | -0.01 | ✓·✓lb |
| case4619_goc | api | 4619 | 1010784.9 | 1010800.0 | 971704.9 | 1068800.0 | -0.01 | ✓·✓lb |
| case4619_goc | sad | 4619 | — | — | 474687.4 | 484350.0 | -0.01 | inf✓·✓lb |
| case4619_goc | typ | 4619 | 457436.6 | 457440.0 | 472392.3 | 476700.0 | -0.01 | ✓·✓lb |
| case4661_sdet | api | 4661 | 2670623.1 | 2670600.0 | 2623054.3 | 2731500.0 | 0.00 | ✓·✓lb |
| case4661_sdet | sad | 4661 | — | — | 2216647.8 | 2261000.0 | 0.00 | inf✓·✓lb |
| case4661_sdet | typ | 4661 | 2216303.9 | 2216300.0 | 2206725.8 | 2251300.0 | -0.01 | ✓·✓lb |
| case4837_goc | api | 4837 | 1209606.3 | 1209600.0 | 1200021.1 | 1291900.0 | -0.01 | ✓·✓lb |
| case4837_goc | sad | 4837 | — | — | 869666.7 | 877120.0 | -0.00 | inf✓·✓lb |
| case4837_goc | typ | 4837 | 850397.1 | 850400.0 | 868168.2 | 872260.0 | -0.00 | ✓·✓lb |
| case4917_goc | api | 4917 | 1703464.0 | 1703500.0 | 1434729.5 | 1717400.0 | 0.08 | ✓·✓lb |
| case4917_goc | sad | 4917 | 1384325.4 | 1384300.0 | 1354002.9 | 1389000.0 | -0.00 | ✓·✓lb |
| case4917_goc | typ | 4917 | 1383656.1 | 1383700.0 | 1353066.3 | 1387800.0 | 0.00 | ✓·✓lb |
| case5658_epigrids | api | 5658 | 1306345.0 | 1306300.0 | 1318822.6 | 1326800.0 | 0.00 | ✓·✓lb |
| case5658_epigrids | sad | 5658 | — | — | 1206615.6 | 1235800.0 | 0.00 | inf✓·✓lb |
| case5658_epigrids | typ | 5658 | 1195466.5 | 1195500.0 | 1205418.3 | 1207300.0 | -0.00 | ✓·✓lb |
| case6468_rte | api | 6468 | 2343290.4 | 2343300.0 | 2436575.4 | 2452700.0 | 0.01 | ✓·✓lb |
| case6468_rte | sad | 6468 | 1982819.8 | 1982800.0 | 2046409.5 | 2069700.0 | 0.01 | ✓·✓lb |
| case6468_rte | typ | 6468 | 1982819.8 | 1982800.0 | 2046150.9 | 2069700.0 | 0.01 | ✓·✓lb |
| case6470_rte | api | 6470 | 2604137.7 | 2604100.0 | 2685118.4 | 2720900.0 | 0.01 | ✓·✓lb |
| case6470_rte | sad | 6470 | 2139078.9 | 2139100.0 | 2198690.4 | 2241600.0 | 0.00 | ✓·✓lb |
| case6470_rte | typ | 6470 | 2136096.9 | 2136100.0 | 2198106.4 | 2237600.0 | 0.01 | ✓·✓lb |
| case6495_rte | api | 6495 | 2924495.6 | 2924500.0 | 3015652.0 | 3130400.0 | 0.01 | ✓·✓lb |
| case6495_rte | sad | 6495 | 2561805.3 | 2561800.0 | 2604047.9 | 3067800.0 | 0.01 | ✓·✓lb |
| case6495_rte | typ | 6495 | 2561788.8 | 2561800.0 | 2604047.9 | 3067800.0 | 0.01 | ✓·✓lb |
| case6515_rte | api | 6515 | 2959744.8 | 2959700.0 | 3057632.1 | 3129200.0 | 0.01 | ✓·✓lb |
| case6515_rte | sad | 6515 | 2559524.4 | 2559500.0 | 2644411.0 | 2869800.0 | 0.00 | ✓·✓lb |
| case6515_rte | typ | 6515 | 2559330.7 | 2559300.0 | 2644404.0 | 2825500.0 | 0.01 | ✓·✓lb |
| case7336_epigrids | api | 7336 | 1980097.5 | 1980100.0 | 1998086.3 | 2035500.0 | -0.00 | ✓·✓lb |
| case7336_epigrids | sad | 7336 | — | — | 1878684.1 | 1888400.0 | -0.01 | inf✓·✓lb |
| case7336_epigrids | typ | 7336 | 1855900.1 | 1855900.0 | 1878683.5 | 1882400.0 | -0.00 | ✓·✓lb |
| case8387_pegase | api | 8387 | 4974002.4 | 4975900.0 | 4637519.2 | 5242800.0 | 1.42 | ✓·lb |
| case8387_pegase | sad | 8387 | 2595938.7 | 2597700.0 | 977279.0 | 2803900.0 | 5.43 | ✓·lb |
| case8387_pegase | typ | 8387 | 2501101.0 | 2502800.0 | 822867.9 | 2771400.0 | 6.20 | ✓·lb |
| case9241_pegase | api | 9241 | 6814526.0 | 6816300.0 | 6840605.9 | 7067900.0 | 0.27 | ✓·✓lb |
| case9241_pegase | sad | 9241 | — | — | 6084311.7 | 6318500.0 | 1.24 | inf✓·lb |
| case9241_pegase | typ | 9241 | 6027173.8 | 6028700.0 | 6075800.7 | 6243100.0 | 0.14 | ✓·✓lb |
| case9591_goc | api | 9591 | 1470245.0 | 1470200.0 | 1346495.0 | 1570300.0 | -0.01 | ✓·✓lb |
| case9591_goc | sad | 9591 | — | — | 1055855.4 | 1167400.0 | -0.01 | inf✓·✓lb |
| case9591_goc | typ | 9591 | 1030938.8 | 1030900.0 | 1055119.5 | 1061700.0 | -0.00 | ✓·✓lb |
| case10000_goc | api | 10000 | 2499133.4 | 2499100.0 | — | — | — | ✓·— |
| case10000_goc | sad | 10000 | — | — | — | — | — | inf✓·— |
| case10000_goc | typ | 10000 | 1346114.3 | 1346100.0 | — | — | — | ✓·— |
| case10192_epigrids | api | 10189 | 1856478.6 | 1856500.0 | 1849684.2 | 1977700.0 | -0.01 | ✓·✓lb |
| case10192_epigrids | sad | 10189 | — | — | 1673015.6 | 1720200.0 | -0.01 | inf✓·✓lb |
| case10192_epigrids | typ | 10189 | 1665551.1 | 1665600.0 | 1672591.5 | 1686900.0 | -0.00 | ✓·✓lb |
| case10480_goc | api | 10480 | 2712412.5 | 2712400.0 | 2709085.2 | 2863500.0 | -0.01 | ✓·✓lb |
| case10480_goc | sad | 10480 | — | — | 2286465.7 | 2314700.0 | -0.01 | inf✓·✓lb |
| case10480_goc | typ | 10480 | 2215826.2 | 2215800.0 | 2286386.9 | 2314600.0 | -0.01 | ✓·✓lb |
| case13659_pegase | api | 13659 | 9117036.9 | 9126300.0 | 9198494.6 | 9385800.0 | 0.15 | ✓·✓lb |
| case13659_pegase | sad | 13659 | — | — | 8829708.1 | 9042200.0 | 0.67 | inf✓·lb |
| case13659_pegase | typ | 13659 | 8763111.4 | 8769900.0 | 8817544.3 | 8948000.0 | 0.07 | ✓·✓lb |
| case19402_goc | api | 19402 | 2458064.0 | 2458100.0 | 2449028.3 | 2583700.0 | -0.01 | ✓·✓lb |
| case19402_goc | sad | 19402 | 1910224.6 | 1910200.0 | 1954400.7 | 1983800.0 | -0.01 | ✓·✓lb |
| case19402_goc | typ | 19402 | 1897794.8 | 1897800.0 | 1954308.1 | 1977800.0 | -0.00 | ✓·✓lb |
| case20758_epigrids | api | 20758 | 3034846.9 | 3034800.0 | 3042940.7 | 3126500.0 | -0.01 | ✓·✓lb |
| case20758_epigrids | sad | 20758 | — | — | 2612726.1 | 2638200.0 | -0.00 | inf✓·✓lb |
| case20758_epigrids | typ | 20758 | 2572328.1 | 2572300.0 | 2608669.6 | 2618600.0 | -0.01 | ✓·✓lb |
| case24464_goc | api | 24464 | — | — | 2560710.2 | 2684000.0 | -0.01 | —·✓lb |
| case24464_goc | sad | 24464 | — | — | 2605377.1 | 2654000.0 | -0.01 | —·✓lb |
| case24464_goc | typ | 24464 | 2512811.8 | 2512800.0 | 2604171.3 | 2629500.0 | -0.01 | ✓·✓lb |
| case30000_goc | api | 30000 | 1700874.2 | 1700900.0 | — | — | — | ✓·— |
| case30000_goc | sad | 30000 | 1297528.4 | 1297500.0 | — | — | — | ✓·— |
| case30000_goc | typ | 30000 | 1092116.1 | 1092100.0 | — | — | — | ✓·— |
Sensitivity parity (finite differences)
Per size band. adj−fwd (worst) is the adjoint/forward solve-consistency bound — the analytic guarantee, near machine precision. FdClean and coupled are the central-difference relative errors per parity class (coupled = Jabr-cone soft cells), shown as median/worst. The median is the validation signal: the typical agreement in the smooth interior. The worst is an outlier where the two-sided difference straddles a non-smooth point — an LMP at a congestion boundary, where the sensitivity is genuinely one-sided and a central difference is not a valid check, or a soft Jabr-cone direction. These are finite-difference limitations, not analytic errors; the analytic columns are pinned by adjoint == forward and by the median. Columns below the regularization floor are skipped.
| band | formulation | cases | cells | FD cols | worst adj−fwd | FdClean med/worst | coupled med/worst |
|---|---|---|---|---|---|---|---|
| 100–1k | ac | 30 | 51 | 294 | 7.4898e-14 | 8.4965e-9 / 8.7898e-7 | — |
| 100–1k | dc | 30 | 22 | 16 | 2.6468e-13 | 4.4498e-2 / 9.2257e-1 | — |
| 100–1k | socwr | 30 | 300 | 1127 | 1.6558e-7 | 2.6745e-3 / 5.1572e5 | 8.4129e-2 / 4.1153e2 |
| 1k–10k | ac | 3 | 6 | 36 | 1.6549e-15 | 7.1479e-9 / 9.2028e1 | — |
| 1k–10k | dc | 3 | 2 | 1 | 8.6689e-21 | 8.0256e-5 / 8.0256e-5 | — |
| 1k–10k | socwr | 3 | 30 | 116 | 1.3965e-10 | 1.9303e-1 / 1.3502e0 | 1.7219e0 / 6.1760e0 |
| <100 | ac | 33 | 78 | 329 | 1.1102e-15 | 1.4183e-8 / 2.6527e-6 | — |
| <100 | dc | 33 | 26 | 48 | 1.6409e-10 | 4.0039e-6 / 1.1623e1 | — |
| <100 | socwr | 33 | 330 | 999 | 9.8460e-7 | 4.9246e-5 / 3.4204e1 | 3.9313e-3 / 2.8670e2 |
Performance (wall time per stage)
Median milliseconds per stage, by size band. Solves are single-threaded.
| band | cases | parse | build | DC | SOCWR | AC PF | sens |
|---|---|---|---|---|---|---|---|
| <100 | 33 | 0.08 | 0.04 | 0.74 | 4.73 | 0.22 | 385.35 |
| 100–1k | 30 | 0.28 | 0.18 | 7.64 | 65.45 | 9.60 | 6125.20 |
| 1k–10k | 108 | 2.81 | 2.13 | 165.68 | 1444.30 | 507.97 | 0.00 |
| >10k | 24 | 17.78 | 21.60 | 1297.56 | 10187.04 | 3892.62 | 0.00 |
Limits and skips
Every capped, failed, or caveated case, with its reason (no silent truncation).
| case | var | buses | status | notes |
|---|---|---|---|---|
| case5_pjm | sad | 5 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf. |
| case14_ieee | sad | 14 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf. |
| case30_as | sad | 30 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf. |
| case30_ieee | sad | 30 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf. |
| case57_ieee | sad | 57 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf. |
| case60_c | sad | 60 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf. |
| case89_pegase | sad | 89 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf. |
| case118_ieee | sad | 118 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf. |
| case179_goc | sad | 179 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 4.857e1 over 5 starts |
| case197_snem | sad | 197 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf. |
| case200_activ | sad | 200 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf. |
| case240_pserc | sad | 240 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 7.232e1 over 5 starts |
| case500_goc | sad | 500 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf. |
| case588_sdet | sad | 588 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf. |
| case793_goc | sad | 793 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf. |
| case1354_pegase | sad | 1354 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf. |
| case1803_snem | sad | 1803 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 1.519e0 over 5 starts; sensitivity skipped: buses 1803 exceed –max-sens-bus 1500 |
| case1951_rte | sad | 1951 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 5.113e1 over 5 starts; sensitivity skipped: buses 1951 exceed –max-sens-bus 1500 |
| case2000_goc | sad | 2000 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 1.828e0 over 5 starts; sensitivity skipped: buses 2000 exceed –max-sens-bus 1500 |
| case2312_goc | sad | 2312 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; sensitivity skipped: buses 2312 exceed –max-sens-bus 1500 |
| case2383wp_k | sad | 2383 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; sensitivity skipped: buses 2383 exceed –max-sens-bus 1500 |
| case2736sp_k | sad | 2736 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; sensitivity skipped: buses 2736 exceed –max-sens-bus 1500 |
| case2737sop_k | sad | 2737 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; sensitivity skipped: buses 2737 exceed –max-sens-bus 1500 |
| case2746wop_k | sad | 2746 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; sensitivity skipped: buses 2746 exceed –max-sens-bus 1500 |
| case2746wp_k | sad | 2746 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; sensitivity skipped: buses 2746 exceed –max-sens-bus 1500 |
| case2848_rte | sad | 2848 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 5.923e-1 over 5 starts; sensitivity skipped: buses 2848 exceed –max-sens-bus 1500 |
| case2853_sdet | sad | 2853 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 1.030e1 over 5 starts; sensitivity skipped: buses 2853 exceed –max-sens-bus 1500 |
| case2868_rte | sad | 2868 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 3.169e1 over 5 starts; sensitivity skipped: buses 2868 exceed –max-sens-bus 1500 |
| case2869_pegase | sad | 2869 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; sensitivity skipped: buses 2869 exceed –max-sens-bus 1500 |
| case3012wp_k | sad | 3012 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 1.335e0 over 5 starts; sensitivity skipped: buses 3012 exceed –max-sens-bus 1500 |
| case3120sp_k | sad | 3120 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; sensitivity skipped: buses 3120 exceed –max-sens-bus 1500 |
| case3970_goc | sad | 3970 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; sensitivity skipped: buses 3970 exceed –max-sens-bus 1500 |
| case4020_goc | sad | 4020 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 2.905e0 over 5 starts; sensitivity skipped: buses 4020 exceed –max-sens-bus 1500 |
| case4619_goc | sad | 4619 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; sensitivity skipped: buses 4619 exceed –max-sens-bus 1500 |
| case4661_sdet | sad | 4661 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 6.734e-1 over 5 starts; sensitivity skipped: buses 4661 exceed –max-sens-bus 1500 |
| case4837_goc | sad | 4837 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 8.525e0 over 5 starts; sensitivity skipped: buses 4837 exceed –max-sens-bus 1500 |
| case5658_epigrids | sad | 5658 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; sensitivity skipped: buses 5658 exceed –max-sens-bus 1500 |
| case7336_epigrids | sad | 7336 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; sensitivity skipped: buses 7336 exceed –max-sens-bus 1500 |
| case9241_pegase | sad | 9241 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 6.289e1 over 5 starts; sensitivity skipped: buses 9241 exceed –max-sens-bus 1500 |
| case9591_goc | sad | 9591 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 7.825e0 over 5 starts; sensitivity skipped: buses 9591 exceed –max-sens-bus 1500 |
| case10000_goc | api | 10000 | caveat | SOCWR solve failed: DC OPF solve did not converge: NumericalError; AC power flow did not converge: best mismatch 5.306e0 over 5 starts; sensitivity skipped: buses 10000 exceed –max-sens-bus 1500 |
| case10000_goc | sad | 10000 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; SOCWR solve failed: DC OPF solve did not converge: NumericalError; AC power flow did not converge: best mismatch 1.452e1 over 5 starts; sensitivity skipped: buses 10000 exceed –max-sens-bus 1500 |
| case10000_goc | typ | 10000 | caveat | SOCWR solve failed: DC OPF solve did not converge: NumericalError; AC power flow did not converge: best mismatch 1.452e1 over 5 starts; sensitivity skipped: buses 10000 exceed –max-sens-bus 1500 |
| case10192_epigrids | sad | 10189 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; bus count 10189 differs from BASELINE nodes 10192; AC power flow did not converge: best mismatch 1.441e1 over 5 starts; sensitivity skipped: buses 10192 exceed –max-sens-bus 1500 |
| case10480_goc | sad | 10480 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 5.689e0 over 5 starts; sensitivity skipped: buses 10480 exceed –max-sens-bus 1500 |
| case13659_pegase | sad | 13659 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 2.786e1 over 5 starts; sensitivity skipped: buses 13659 exceed –max-sens-bus 1500 |
| case20758_epigrids | sad | 20758 | caveat | DC infeasible (DC OPF solve infeasible: PrimalInfeasible); consistent with BASELINE inf.; AC power flow did not converge: best mismatch 2.751e-1 over 5 starts; sensitivity skipped: buses 20758 exceed –max-sens-bus 1500 |
| case24464_goc | api | 24464 | failed | DC OPF solve failed: DC OPF solve did not converge: NumericalError; AC power flow did not converge: best mismatch 1.699e1 over 5 starts; sensitivity skipped: buses 24464 exceed –max-sens-bus 1500 |
| case24464_goc | sad | 24464 | failed | DC OPF solve failed: DC OPF solve did not converge: NumericalError; AC power flow did not converge: best mismatch 2.075e1 over 5 starts; sensitivity skipped: buses 24464 exceed –max-sens-bus 1500 |
| case30000_goc | api | 30000 | caveat | SOCWR solve failed: DC OPF solve did not converge: NumericalError; AC power flow did not converge: best mismatch 3.598e0 over 5 starts; sensitivity skipped: buses 30000 exceed –max-sens-bus 1500 |
| case30000_goc | sad | 30000 | caveat | SOCWR solve failed: DC OPF solve did not converge: NumericalError; AC power flow did not converge: best mismatch 1.198e1 over 5 starts; sensitivity skipped: buses 30000 exceed –max-sens-bus 1500 |
| case30000_goc | typ | 30000 | caveat | SOCWR solve failed: DC OPF solve did not converge: NumericalError; AC power flow did not converge: best mismatch 1.198e1 over 5 starts; sensitivity skipped: buses 30000 exceed –max-sens-bus 1500 |
| case78484_epigrids | api | 78484 | skipped | timed out after 180s |
| case78484_epigrids | sad | 78484 | skipped | timed out after 180s |
| case78484_epigrids | typ | 78484 | skipped | timed out after 180s |
198 rows; 55 skipped/failed/caveat.