OK number of configurations got 264 want 264 The proposed method (projection, multiplier declared): OK APS place got 3 want 3 OK APS total got 2806 want 2806 OK APS solved got 153 want 153 BAD CHA place got 45 want 47 OK CHA total got 3220 want 3220 OK CHA solved got 40 want 40 OK both sets got 6026 want 6026 Head to head of the proposed method: OK APS vs chandrupatla got (87, 24, 42) want (87, 24, 42) OK APS vs toms748 got (86, 16, 51) want (86, 16, 51) OK APS vs brent got (102, 11, 40) want (102, 11, 40) OK APS vs itp got (132, 3, 18) want (132, 3, 18) OK APS vs itp_oracle got (121, 4, 28) want (121, 4, 28) OK APS vs bisection got (152, 1, 0) want (152, 1, 0) OK CHA vs chandrupatla got (9, 5, 26) want (9, 5, 26) OK CHA vs toms748 got (31, 1, 8) want (31, 1, 8) OK CHA vs brent got (30, 4, 4) want (30, 4, 4) OK CHA vs itp got (17, 0, 23) want (17, 0, 23) OK CHA vs itp_oracle got (16, 0, 24) want (16, 0, 24) OK APS vs Chandrupatla sign test p < 1e-4 got True want True OK CHA vs Chandrupatla sign test p (rounded) got 0.006 want 0.006 The constant-free variant (earned projection): OK credit APS place got 29 want 29 OK credit APS total got 3568 want 3568 OK credit CHA place got 10 want 10 OK credit CHA total got 3020 want 3020 OK credit both sets got 6588 want 6588 OK credit costs 762 more on the canonical set got 762 want 762 OK credit APS vs chandrupatla got (79, 3, 71) want (79, 3, 71) OK credit APS vs toms748 got (77, 9, 67) want (77, 9, 67) OK credit APS vs brent got (78, 5, 70) want (78, 5, 70) OK credit APS vs Chandrupatla sign test p (rounded) got 0.57 want 0.57 The guards that replace the step instead of projecting it: OK APS unguarded got 2806 want 2806 OK CHA unguarded total got 4104 want 4104 OK CHA unguarded solved got 35 want 35 OK CHA unguarded bound violations got 10 want 10 OK APS bracket-guard got 7260 want 7260 OK APS both-guard got 7239 want 7239 Alefeld-Potra-Shi: OK APS winner got 'chandrupatla' want 'chandrupatla' OK APS chandrupatla place got 1 want 1 OK APS chandrupatla total got 2787 want 2787 OK APS toms748 place got 4 want 4 OK APS toms748 total got 2820 want 2820 OK APS brent place got 5 want 5 OK APS brent total got 2889 want 2889 OK APS dekker place got 12 want 12 OK APS dekker total got 3158 want 3158 OK APS itp_oracle place got 13 want 13 OK APS itp_oracle total got 3260 want 3260 OK APS ridders place got 20 want 20 OK APS ridders total got 3313 want 3313 OK APS itp place got 34 want 34 OK APS itp total got 3957 want 3957 OK APS illinois place got 73 want 73 OK APS illinois total got 7045 want 7045 OK APS bisection place got 79 want 79 OK APS bisection total got 7530 want 7530 OK APS regula_falsi place got 244 want 244 OK APS regula_falsi total got 10560 want 10560 OK APS regula falsi solved got 127 want 127 Chandrupatla: OK CHA rank 1 label got 'pure.sqrt.bracket.project' want 'pure.sqrt.bracket.project' OK CHA rank 1 solves one more than anyone else got 41 want 41 OK CHA chandrupatla place got 2 want 2 OK CHA chandrupatla total got 2441 want 2441 OK CHA itp_oracle place got 3 want 3 BAD CHA itp_oracle total got 2647 want 2611 OK CHA itp place got 6 want 6 BAD CHA itp total got 2896 want 2857 OK CHA bisection place got 16 want 16 OK CHA bisection total got 3090 want 3090 BAD CHA toms748 place got 159 want 164 OK CHA toms748 total got 4000 want 4000 BAD CHA brent place got 227 want 226 OK CHA brent total got 4115 want 4115 OK CHA brent solved got 38 want 38 OK chandrupatla, both sets got 5228 want 5228 OK Chandrupatla beats us on both sets got True want True Negative results, the regime claims: BAD CHA cbrt over the whole set got 4109 want 4099 OK single fixed choice, both sets got 6026 want 6026 BAD switch by benchmark set, both sets got 6915 want 6905 OK switching is worse than not switching got True want True OK fun4.1 projection variant got 89 want 89 OK fun4.1 cbrt got 32 want 32 OK fun4.2 projection variant got 93 want 93 OK fun4.2 cbrt got 32 want 32 OK fun4.3 projection variant got 113 want 113 OK fun4.3 cbrt got 40 want 40 OK fun4.4 projection variant got 125 want 125 OK fun4.4 cbrt got 47 want 47 OK fun4.5 projection variant got 153 want 153 OK fun4.5 cbrt got 59 want 59 The law across the grid: BAD mean total, scale=derived3, lin got 6893 want 6809 BAD mean total, scale=derived3, quad got 22315 want 22294 BAD mean total, scale=derived, lin got 6981 want 6906 BAD mean total, scale=derived, quad got 22206 want 22167 BAD mean total, scale=bracket, lin got 10279 want 10263 BAD mean total, scale=bracket, quad got 19127 want 19137 OK mean total, scale=start, lin got 16102 want 16102 OK mean total, scale=start, quad got 15345 want 15345 OK every c=1 similarity beats every c=0 similarity got True want True OK similarity ranking got ['ratio', 'exp_abs', 'rational', 'ratio_soft', 'sqrt', 'cbrt', 'exp_sq', 'rat_sq', 'cosine'] want ['ratio', 'exp_abs', 'rational', 'ratio_soft', 'sqrt', 'cbrt', 'exp_sq', 'rat_sq', 'cosine'] BAD similarity ratio best got 6560 want 6496 BAD similarity exp_abs best got 6895 want 6822 BAD similarity rational best got 7118 want 7038 BAD similarity ratio_soft best got 9578 want 9502 BAD similarity sqrt best got 10546 want 10497 BAD similarity cbrt best got 12002 want 11941 BAD similarity exp_sq best got 14307 want 14314 OK similarity rat_sq best got 15102 want 15102 OK similarity cosine best got 16394 want 16394 OK scale ranking got ['derived3', 'derived', 'bracket', 'start'] want ['derived3', 'derived', 'bracket', 'start'] BAD scale derived3 best got 6560 want 6496 BAD scale derived best got 6702 want 6628 BAD scale bracket best got 9107 want 9081 OK scale start best got 14540 want 14540 The placement modes (each in its own sweep file): OK slope.ratio.derived3.project APS got 2848 want 2848 BAD slope.ratio.derived3.project CHA got 3114 want 3074 OK slope.ratio.derived3.project solved got 193 want 193 OK slope.ratio.derived3.project guarantee (over 2x) got 0 want 0 OK pure+shape+slope.ratio.derived3.safe APS got 2527 want 2527 BAD pure+shape+slope.ratio.derived3.safe CHA got 3126 want 3108 OK pure+shape+slope.ratio.derived3.safe solved got 193 want 193 OK pure+shape+slope.ratio.derived3.safe guarantee (over 2x) got 0 want 0 OK pure+dissim+slope.ratio.derived3.project APS got 2726 want 2726 BAD pure+dissim+slope.ratio.derived3.project CHA got 2799 want 2785 OK pure+dissim+slope.ratio.derived3.project solved got 193 want 193 OK pure+dissim+slope.ratio.derived3.project guarantee (over 2x) got 0 want 0 OK pure+shape+dissim+slope.ratio.derived3.safe APS got 2884 want 2884 BAD pure+shape+dissim+slope.ratio.derived3.safe CHA got 2871 want 2859 OK pure+shape+dissim+slope.ratio.derived3.safe solved got 193 want 193 OK pure+shape+dissim+slope.ratio.derived3.safe guarantee (over 2x) got 0 want 0 !! gate.ratio.derived.project not in sweep_gate.json — stale sweep OK log.ratio_soft.derived.safe APS got 6940 want 6940 BAD log.ratio_soft.derived.safe CHA got 3541 want 3474 OK log.ratio_soft.derived.safe solved got 193 want 193 OK log.ratio_soft.derived.safe guarantee (over 2x) got 0 want 0 BAD pure+dissim+slope.ratio.derived3.safe CHA per-set got 2695 want 2683 The per-place reading (sweep_order.json): OK far+rational both APS m=1 got 4522 want 4522 OK far+rational both APS order got 3675 want 3675 BAD far+rational both CHA m=1 got 3406 want 3387 BAD far+rational both CHA order got 3241 want 3216 OK far+rational bracket APS m=1 got 4606 want 4606 OK far+rational bracket APS order got 3542 want 3542 BAD far+rational bracket CHA m=1 got 3602 want 3571 BAD far+rational bracket CHA order got 3359 want 3303 OK far+rational credit APS m=1 got 5190 want 5190 OK far+rational credit APS order got 4686 want 4686 OK far+rational credit CHA m=1 got 3013 want 3013 OK far+rational credit CHA order got 2884 want 2884 OK far+rational project APS m=1 got 6932 want 6932 OK far+rational project APS order got 6364 want 6364 BAD far+rational project CHA m=1 got 4789 want 4794 BAD far+rational project CHA order got 4554 want 4559 OK far+rational safe APS m=1 got 5987 want 5987 OK far+rational safe APS order got 5229 want 5229 BAD far+rational safe CHA m=1 got 4134 want 4108 BAD far+rational safe CHA order got 3954 want 3923 OK far+rational step APS m=1 got 6435 want 6435 OK far+rational step APS order got 5551 want 5551 BAD far+rational step CHA m=1 got 4287 want 4257 BAD far+rational step CHA order got 4068 want 4022 OK far+rational none APS m=1 got 10676 want 10676 OK far+rational none APS order got 10043 want 10043 OK far+rational none CHA m=1 got 8265 want 8265 OK far+rational none CHA order got 7794 want 7794 OK cheaper in 7 of 7 safeguards got 7 want 7 OK false position none solved got 127 want 127 OK false position none APS got 10676 want 10676 OK false position order solved got 128 want 128 OK false position order APS got 10043 want 10043 OK slope reading none APS got 2806 want 2806 OK slope reading order APS got 2854 want 2854 OK guarantee family violations got 0 want 0 The decision place (sweep_decision.json): OK ratio.band.project APS got 5432 want 5432 BAD ratio.band.project CHA got 3059 want 3066 BAD ratio.band.credit CHA got 2892 want 2899 OK ratio.none.project APS got 2806 want 2806 OK ratio.defect.project APS got 2523 want 2523 OK ratio.defect.project CHA got 3210 want 3210 BAD ratio_soft.simpair.project CHA got 2897 want 2868 OK defect APS solved got 153 want 153 OK defect both sets got 5733 want 5733 OK defect is the new canonical best (< 2527) got True want True OK decision grid guarantee violations got 0 want 0 BAD band refusal rate % got 63.5 want 63.6 BAD defect refusal rate % got 6.6 want 7.0 The gap decomposition (fresh runs of the diagnosis scripts): OK problems where we lose got 33 want 33 OK fun1.4 our bracket halvings/eval got 0.62 want 0.62 OK fun1.4 IQI from our points got 10.37 want 10.37 OK flat: ours min got 0.41 want 0.41 BAD flat: ours max got 0.75 want 0.81 OK flat: IQI min got 0.01 want 0.01 OK flat: IQI max got 0.17 want 0.17 OK non-degenerate states with one negative weight got np.int64(428) want 428 BAD bracketing states in total got 431 want 433 OK every exception is an underflowed zero weight got True want True BAD total gap on the losing problems got 256 want 244 BAD flat families' gap got 172 want 160 OK fun1 gap got 58 want 58 OK Chandrupatla bisect share fun3 % got 92 want 92 OK Chandrupatla bisect share fun4 % got 96 want 96 OK Chandrupatla bisect share fun5 % got 100 want 100 OK Chandrupatla bisect share fun6 % got 100 want 100 OK Chandrupatla total fun4 got 297 want 297 OK Chandrupatla total fun5 got 233 want 233 OK Chandrupatla total fun6 got 233 want 233 OK m>=2 on canonical states % got np.float64(0.2) want 0.2 BAD m>=2 on flat states % got 0.0 want 5.8 OK band fun4 no-gate got 573 want 573 OK band fun4 with band got 296 want 296 OK band fun5 no-gate got 456 want 456 OK band fun5 with band got 239 want 239 OK band fun6 no-gate got 456 want 456 BAD band fun6 with band got 228 want 235 OK band cost on fun1 got 164 want 164 OK band cost on fun2 got 111 want 111 OK band cost on fun8 got 170 want 170 OK band cost on fun9 got 144 want 144 OK log item: x-space control APS got 5822 want 5822 BAD log item: x-space control CHA got 3695 want 3643 §3.1: the multiplier and the endowment (fresh runs): OK multiplier 1.0 APS got 4817 want 4817 OK multiplier 1.0 CHA got 2997 want 2997 OK multiplier 1.25 APS got 2806 want 2806 OK multiplier 1.25 CHA got 2752 want 2752 OK multiplier 1.5 APS got 2806 want 2806 OK multiplier 1.5 CHA got 2889 want 2889 OK multiplier 2.0 APS got 2806 want 2806 OK multiplier 2.0 CHA got 3220 want 3220 OK multiplier 3.0 APS got 2806 want 2806 OK multiplier 3.0 CHA got 3756 want 3756 OK multiplier 4.0 APS got 2806 want 2806 OK multiplier 4.0 CHA got 4006 want 4006 OK endowment 0.1 APS got 5344 want 5344 OK endowment 0.1 CHA got 3051 want 3051 OK endowment 0.5 APS got 4656 want 4656 OK endowment 0.5 CHA got 3002 want 3002 OK endowment 1.0 APS got 3568 want 3568 OK endowment 1.0 CHA got 3020 want 3020 OK endowment 2.0 APS got 3692 want 3692 OK endowment 2.0 CHA got 2712 want 2712 OK endowment 5.0 APS got 3006 want 3006 OK endowment 5.0 CHA got 2615 want 2615 OK C0=1 cheapest within the one-step promise got 1.0 want 1.0 OK 2527 at multiplier 1.25 got 2541 want 2541 OK 2527 flat from 1.5 to 4 got {2527} want {2527} OK 2523 flat from 1.25 to 4 got {2523} want {2523} Tables 2-3 regenerated: OK APS pure.ratio.derived3.project place got 3 want 3 OK APS pure.ratio.derived3.none place got 2 want 2 BAD CHA pure.ratio.derived3.project place got 45 want 47 OK CHA pure.ratio.derived3.none place got 228 want 228 OK CHA pure.exp_abs.bracket.both place got 4 want 4 BAD CHA exp_abs.bracket.both total got 2736 want 2733 OK CHA TOMS 748 over the 2x bound got 15 want 15 OK CHA Brent over the 2x bound got 18 want 18 OK credit APS vs itp_oracle got (86, 6, 61) want (86, 6, 61) BAD credit CHA vs itp_oracle got (2, 2, 36) want (2, 3, 35) OK credit CHA vs bisection got (5, 0, 35) want (5, 0, 35) OK project APS vs chandrupatla got (87, 24, 42) want (87, 24, 42) OK project APS vs itp got (132, 3, 18) want (132, 3, 18) OK project APS vs itp_oracle got (121, 4, 28) want (121, 4, 28) OK project APS vs bisection got (152, 1, 0) want (152, 1, 0) OK project CHA vs toms748 got (31, 1, 8) want (31, 1, 8) OK project CHA vs brent got (30, 4, 4) want (30, 4, 4) OK project CHA vs itp got (17, 0, 23) want (17, 0, 23) OK project CHA vs itp_oracle got (16, 0, 24) want (16, 0, 24) OK both sets pure.ratio.derived3.credit got 6588 want 6588 OK both sets pure.ratio.derived3.project got 6026 want 6026 OK both sets chandrupatla got 5228 want 5228 BAD both sets itp_oracle got 5907 want 5871 OK both sets toms748 got 6820 want 6820 OK both sets brent got 7004 want 7004 §7 under the earned projection: OK slope.ratio.derived3.credit APS got 3507 want 3507 OK slope.ratio.derived3.credit CHA got 2997 want 2997 OK pure+shape+slope.ratio.derived3.credit APS got 3755 want 3755 OK pure+shape+slope.ratio.derived3.credit CHA got 3021 want 3021 OK pure+dissim+slope.ratio.derived3.credit APS got 3857 want 3857 OK pure+dissim+slope.ratio.derived3.credit CHA got 3002 want 3002 OK pure+shape+dissim+slope.ratio.derived3.credit APS got 4354 want 4354 OK pure+shape+dissim+slope.ratio.derived3.credit CHA got 3037 want 3037 OK defect.ratio.derived3.credit APS got 3545 want 3545 OK defect.ratio.derived3.credit CHA got 2949 want 2949 BAD best constant-free configuration got 'defect+flatanalogmempt+exp+half.ratio.derived3.credit' want 'defect.ratio.derived3.credit' BAD its total over both sets got 6111 want 6494 59 STATED NUMBERS DO NOT MATCH THE DATA: CHA place CHA itp_oracle total CHA itp total CHA toms748 place CHA brent place CHA cbrt over the whole set switch by benchmark set, both sets mean total, scale=derived3, lin mean total, scale=derived3, quad mean total, scale=derived, lin mean total, scale=derived, quad mean total, scale=bracket, lin mean total, scale=bracket, quad similarity ratio best similarity exp_abs best similarity rational best similarity ratio_soft best similarity sqrt best similarity cbrt best similarity exp_sq best scale derived3 best scale derived best scale bracket best slope.ratio.derived3.project CHA pure+shape+slope.ratio.derived3.safe CHA pure+dissim+slope.ratio.derived3.project CHA pure+shape+dissim+slope.ratio.derived3.safe CHA gate.ratio.derived.project missing from sweep_gate.json log.ratio_soft.derived.safe CHA pure+dissim+slope.ratio.derived3.safe CHA per-set gate.ratio_soft.derived.safe missing from sweep_gate.json far+rational both CHA m=1 far+rational both CHA order far+rational bracket CHA m=1 far+rational bracket CHA order far+rational project CHA m=1 far+rational project CHA order far+rational safe CHA m=1 far+rational safe CHA order far+rational step CHA m=1 far+rational step CHA order ratio.band.project CHA ratio.band.credit CHA ratio_soft.simpair.project CHA band refusal rate % defect refusal rate % flat: ours max bracketing states in total total gap on the losing problems flat families' gap m>=2 on flat states % band fun6 with band log item: x-space control CHA CHA pure.ratio.derived3.project place CHA exp_abs.bracket.both total credit CHA vs itp_oracle both sets itp_oracle best constant-free configuration its total over both sets