Details

analyze2.1s (8.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 19 to 19 computations (0% saved)

sample57.0ms (0.2%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
7.0ms	92×	body	128	nan
3.0ms	45×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify130.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

645×	`distribute-neg-frac_binary64_1065`
581×	`distribute-rgt-neg-in_binary64_1059`
569×	`distribute-lft-neg-in_binary64_1058`
418×	`associate-/l*_binary64_1046`
372×	`cancel-sign-sub-inv_binary64_1067`
251×	`associate-/l/_binary64_1048`
237×	`*-commutative_binary64_1032`
227×	`times-frac_binary64_1107`
191×	`associate-/r/_binary64_1047`
163×	`associate-/r*_binary64_1045`
133×	`neg-mul-1_binary64_1097`
132×	`neg-sub0_binary64_1096`
91×	`associate-*l/_binary64_1044`
77×	`associate-l_binary64_1042`
73×	`associate-*r/_binary64_1043`
69×	`associate-r_binary64_1041`
55×	`div-sub_binary64_1106`
31×	`sub-neg_binary64_1094`
22×	`distribute-lft-neg-out_binary64_1060`
20×	`swap-sqr_binary64_1068`
18×	`distribute-rgt-neg-out_binary64_1061`
15×	`distribute-frac-neg_binary64_1064`
8×	`unswap-sqr_binary64_1069`
7×	`sqr-pow_binary64_1073`
4×	`unsub-neg_binary64_1095`
3×	`+-commutative_binary64_1031`
2×	`pow-plus_binary64_1164` `cube-unmult_binary64_1138` `mul0-rgt_binary64_1084` `mul0-lft_binary64_1083` `div0_binary64_1082` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`
1×	`unpow2_binary64_1166` `unpow1/2_binary64_1165` `unpow1_binary64_1159` `1-exp_binary64_1145` `rem-sqrt-square_binary64_1114` `sub0-neg_binary64_1088` `associate-+l-_binary64_1036` `associate-+l+_binary64_1034`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1364` `erf-erfc_binary64_1363` `erf-odd_binary64_1362` `if-if-and-not_binary64_1361` `if-if-and_binary64_1360` `if-if-or-not_binary64_1359` `if-if-or_binary64_1358` `if-not_binary64_1357` `if-same_binary64_1356` `if-false_binary64_1355` `if-true_binary64_1354` `not-gte_binary64_1353` `not-lte_binary64_1352` `not-gt_binary64_1351` `not-lt_binary64_1350` `gte-same_binary64_1349` `lte-same_binary64_1348` `gt-same_binary64_1347` `lt-same_binary64_1346` `sinh---cosh_binary64_1293` `sinh-+-cosh_binary64_1292` `sinh-cosh_binary64_1291` `tanh-def-c_binary64_1290` `tanh-def-b_binary64_1289` `tanh-def-a_binary64_1288` `cosh-def_binary64_1287` `sinh-def_binary64_1286` `tan-neg_binary64_1233` `cos-neg_binary64_1232` `sin-neg_binary64_1231` `tan-0_binary64_1230` `cos-0_binary64_1229` `sin-0_binary64_1228` `hang-m-tan_binary64_1227` `hang-p-tan_binary64_1226` `hang-m0-tan_binary64_1225` `hang-p0-tan_binary64_1224` `hang-0m-tan_binary64_1223` `hang-0p-tan_binary64_1222` `tan-+PI/2_binary64_1221` `tan-+PI_binary64_1220` `tan-PI_binary64_1219` `tan-PI/3_binary64_1218` `tan-PI/4_binary64_1217` `tan-PI/6_binary64_1216` `cos-+PI/2_binary64_1215` `cos-+PI_binary64_1214` `cos-PI_binary64_1213` `cos-PI/2_binary64_1212` `cos-PI/3_binary64_1211` `cos-PI/4_binary64_1210` `cos-PI/6_binary64_1209` `sin-+PI/2_binary64_1208` `sin-+PI_binary64_1207` `sin-PI_binary64_1206` `sin-PI/2_binary64_1205` `sin-PI/3_binary64_1204` `sin-PI/4_binary64_1203` `sin-PI/6_binary64_1202` `sub-1-sin_binary64_1201` `sub-1-cos_binary64_1200` `-1-add-sin_binary64_1199` `-1-add-cos_binary64_1198` `1-sub-sin_binary64_1197` `1-sub-cos_binary64_1196` `cos-sin-sum_binary64_1195` `log-E_binary64_1191` `log-pow_binary64_1190` `log-rec_binary64_1189` `log-div_binary64_1188` `log-prod_binary64_1187` `pow-base-0_binary64_1185` `unpow1/3_binary64_1168` `unpow3_binary64_1167` `exp-to-pow_binary64_1163` `pow-base-1_binary64_1161` `unpow0_binary64_1160` `unpow-1_binary64_1158` `exp-lft-cube_binary64_1157` `exp-lft-sqr_binary64_1156` `exp-cbrt_binary64_1155` `exp-sqrt_binary64_1154` `exp-prod_binary64_1153` `div-exp_binary64_1152` `rec-exp_binary64_1151` `prod-exp_binary64_1150` `exp-diff_binary64_1149` `exp-neg_binary64_1148` `exp-sum_binary64_1147` `e-exp-1_binary64_1146` `exp-1-e_binary64_1144` `exp-0_binary64_1143` `rem-log-exp_binary64_1142` `rem-exp-log_binary64_1141` `cube-mult_binary64_1131` `cube-div_binary64_1130` `cube-prod_binary64_1129` `cube-neg_binary64_1128` `rem-3cbrt-rft_binary64_1127` `rem-3cbrt-lft_binary64_1126` `rem-cbrt-cube_binary64_1125` `rem-cube-cbrt_binary64_1124` `sqr-abs_binary64_1116` `sqr-neg_binary64_1115` `rem-square-sqrt_binary64_1113` `mul-1-neg_binary64_1093` `/-rgt-identity_binary64_1092` `-rgt-identity_binary64_1091` `-lft-identity_binary64_1090` `remove-double-neg_binary64_1089` `--rgt-identity_binary64_1087` `+-rgt-identity_binary64_1086` `+-lft-identity_binary64_1085` `*-inverses_binary64_1081` `+-inverses_binary64_1080` `lft-mult-inverse_binary64_1079` `rgt-mult-inverse_binary64_1078` `remove-double-div_binary64_1077` `pow-sqr_binary64_1074` `difference-of-sqr--1_binary64_1072` `difference-of-sqr-1_binary64_1071` `difference-of-squares_binary64_1070` `cancel-sign-sub_binary64_1066` `distribute-neg-out_binary64_1063` `distribute-neg-in_binary64_1062` `distribute-rgt1-in_binary64_1057` `distribute-lft1-in_binary64_1056` `distribute-rgt-out--_binary64_1055` `distribute-rgt-out_binary64_1054` `distribute-lft-out--_binary64_1053` `distribute-lft-out_binary64_1052` `count-2_binary64_1049` `associate--r-_binary64_1040` `associate--l-_binary64_1039` `associate--l+_binary64_1038` `associate--r+_binary64_1037` `associate-+r-_binary64_1035` `associate-+r+_binary64_1033`

Counts

1 → 3

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	42	27
2	111	27
3	718	27
4	2815	27

prune12.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	2	1	3
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	2	2	4

Error

13.1b

Counts

4 → 2

Compiler

Compiled 90 to 76 computations (15.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
3.1b	(*.f64 (/.f64 M 2) (/.f64 D d))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))
11.0b	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))

rewrite286.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

7.5b

Rules

67×	`add-exp-log_binary64_1139`
58×	`add-sqr-sqrt_binary64_1123`
34×	`times-frac_binary64_1107`
32×	`associate-r_binary64_1041`
30×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
27×	`prod-exp_binary64_1150`
23×	`add-cbrt-cube_binary64_1137`
22×	`associate-l_binary64_1042`
19×	`div-exp_binary64_1152`
12×	`unswap-sqr_binary64_1069`
10×	`pow-exp_binary64_1169`
9×	`pow1_binary64_1162`
7×	`cbrt-unprod_binary64_1134` `sqrt-prod_binary64_1117`
5×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140` `associate-*r/_binary64_1043` `sqrt-div_binary64_1118`
3×	`unpow2_binary64_1166` `sqr-pow_binary64_1073` `div-inv_binary64_1098` `*-commutative_binary64_1032`
2×	`pow-to-exp_binary64_1170` `flip3--_binary64_1105` `flip--_binary64_1076` `pow-prod-down_binary64_1172`
1×	`unpow-prod-down_binary64_1180` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `frac-times_binary64_1111` `associate-*l/_binary64_1044`

Counts

4 → 139

Calls

4 calls:

11.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
10.0ms	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))

Compiler

Compiled 4029 to 2284 computations (43.3% saved)

series1.5s (5.9%)

Error

6.8b

Counts

4 → 57

Calls

4 calls:

578.0ms	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))
466.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
234.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l))))
136.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

Compiler

Compiled 3306 to 2982 computations (9.8% saved)

simplify117.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

353×	`associate-l_binary64_1042`
313×	`associate-r_binary64_1041`
268×	`distribute-rgt-neg-in_binary64_1059`
244×	`distribute-lft-neg-in_binary64_1058`
208×	`associate-*r/_binary64_1043`
201×	`*-commutative_binary64_1032`
200×	`associate-/l*_binary64_1046`
173×	`associate-*l/_binary64_1044`
140×	`distribute-neg-frac_binary64_1065`
128×	`cancel-sign-sub-inv_binary64_1067`
110×	`times-frac_binary64_1107`
107×	`unswap-sqr_binary64_1069`
89×	`log-prod_binary64_1187`
72×	`cube-prod_binary64_1129`
68×	`associate-/r*_binary64_1045`
67×	`exp-prod_binary64_1153`
64×	`sqr-pow_binary64_1073`
59×	`distribute-lft-in_binary64_1050`
58×	`distribute-rgt-in_binary64_1051`
57×	`neg-sub0_binary64_1096`
51×	`neg-mul-1_binary64_1097` `-rgt-identity_binary64_1091` `-lft-identity_binary64_1090` `swap-sqr_binary64_1068`
43×	`log-div_binary64_1188`
40×	`associate-/l/_binary64_1048`
37×	`sub-neg_binary64_1094`
35×	`cube-div_binary64_1130`
29×	`+-commutative_binary64_1031`
19×	`associate-/r/_binary64_1047`
16×	`distribute-rgt-out_binary64_1054`
11×	`/-rgt-identity_binary64_1092` `distribute-lft-neg-out_binary64_1060` `distribute-lft-out_binary64_1052`
10×	`exp-sqrt_binary64_1154`
9×	`associate-+r-_binary64_1035`
8×	`log-pow_binary64_1190` `unpow3_binary64_1167` `rem-sqrt-square_binary64_1114`
7×	`pow-plus_binary64_1164` `cube-unmult_binary64_1138` `distribute-rgt1-in_binary64_1057`
6×	`cube-mult_binary64_1131` `mul-1-neg_binary64_1093` `pow-sqr_binary64_1074` `associate-+l+_binary64_1034`
5×	`unpow2_binary64_1166` `unpow1/2_binary64_1165` `unpow1_binary64_1159` `associate-+l-_binary64_1036`
4×	`distribute-neg-in_binary64_1062`
3×	`distribute-rgt-neg-out_binary64_1061` `associate-+r+_binary64_1033`
2×	`distribute-lft1-in_binary64_1056`
1×	`1-exp_binary64_1145` `exp-1-e_binary64_1144` `rem-square-sqrt_binary64_1113` `associate--r-_binary64_1040` `associate--r+_binary64_1037`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1364` `erf-erfc_binary64_1363` `erf-odd_binary64_1362` `if-if-and-not_binary64_1361` `if-if-and_binary64_1360` `if-if-or-not_binary64_1359` `if-if-or_binary64_1358` `if-not_binary64_1357` `if-same_binary64_1356` `if-false_binary64_1355` `if-true_binary64_1354` `not-gte_binary64_1353` `not-lte_binary64_1352` `not-gt_binary64_1351` `not-lt_binary64_1350` `gte-same_binary64_1349` `lte-same_binary64_1348` `gt-same_binary64_1347` `lt-same_binary64_1346` `sinh---cosh_binary64_1293` `sinh-+-cosh_binary64_1292` `sinh-cosh_binary64_1291` `tanh-def-c_binary64_1290` `tanh-def-b_binary64_1289` `tanh-def-a_binary64_1288` `cosh-def_binary64_1287` `sinh-def_binary64_1286` `tan-neg_binary64_1233` `cos-neg_binary64_1232` `sin-neg_binary64_1231` `tan-0_binary64_1230` `cos-0_binary64_1229` `sin-0_binary64_1228` `hang-m-tan_binary64_1227` `hang-p-tan_binary64_1226` `hang-m0-tan_binary64_1225` `hang-p0-tan_binary64_1224` `hang-0m-tan_binary64_1223` `hang-0p-tan_binary64_1222` `tan-+PI/2_binary64_1221` `tan-+PI_binary64_1220` `tan-PI_binary64_1219` `tan-PI/3_binary64_1218` `tan-PI/4_binary64_1217` `tan-PI/6_binary64_1216` `cos-+PI/2_binary64_1215` `cos-+PI_binary64_1214` `cos-PI_binary64_1213` `cos-PI/2_binary64_1212` `cos-PI/3_binary64_1211` `cos-PI/4_binary64_1210` `cos-PI/6_binary64_1209` `sin-+PI/2_binary64_1208` `sin-+PI_binary64_1207` `sin-PI_binary64_1206` `sin-PI/2_binary64_1205` `sin-PI/3_binary64_1204` `sin-PI/4_binary64_1203` `sin-PI/6_binary64_1202` `sub-1-sin_binary64_1201` `sub-1-cos_binary64_1200` `-1-add-sin_binary64_1199` `-1-add-cos_binary64_1198` `1-sub-sin_binary64_1197` `1-sub-cos_binary64_1196` `cos-sin-sum_binary64_1195` `log-E_binary64_1191` `log-rec_binary64_1189` `pow-base-0_binary64_1185` `unpow1/3_binary64_1168` `exp-to-pow_binary64_1163` `pow-base-1_binary64_1161` `unpow0_binary64_1160` `unpow-1_binary64_1158` `exp-lft-cube_binary64_1157` `exp-lft-sqr_binary64_1156` `exp-cbrt_binary64_1155` `div-exp_binary64_1152` `rec-exp_binary64_1151` `prod-exp_binary64_1150` `exp-diff_binary64_1149` `exp-neg_binary64_1148` `exp-sum_binary64_1147` `e-exp-1_binary64_1146` `exp-0_binary64_1143` `rem-log-exp_binary64_1142` `rem-exp-log_binary64_1141` `cube-neg_binary64_1128` `rem-3cbrt-rft_binary64_1127` `rem-3cbrt-lft_binary64_1126` `rem-cbrt-cube_binary64_1125` `rem-cube-cbrt_binary64_1124` `sqr-abs_binary64_1116` `sqr-neg_binary64_1115` `div-sub_binary64_1106` `unsub-neg_binary64_1095` `remove-double-neg_binary64_1089` `sub0-neg_binary64_1088` `--rgt-identity_binary64_1087` `+-rgt-identity_binary64_1086` `+-lft-identity_binary64_1085` `mul0-rgt_binary64_1084` `mul0-lft_binary64_1083` `div0_binary64_1082` `*-inverses_binary64_1081` `+-inverses_binary64_1080` `lft-mult-inverse_binary64_1079` `rgt-mult-inverse_binary64_1078` `remove-double-div_binary64_1077` `difference-of-sqr--1_binary64_1072` `difference-of-sqr-1_binary64_1071` `difference-of-squares_binary64_1070` `cancel-sign-sub_binary64_1066` `distribute-frac-neg_binary64_1064` `distribute-neg-out_binary64_1063` `distribute-rgt-out--_binary64_1055` `distribute-lft-out--_binary64_1053` `count-2_binary64_1049` `associate--l-_binary64_1039` `associate--l+_binary64_1038`

Counts

196 → 292

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	313	4180
1	773	3999
2	3058	3999

prune443.0ms (1.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	278	14	292
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	279	15	294

Error

3.9b

Counts

294 → 15

Compiler

Compiled 8394 to 4436 computations (47.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.1b	(*.f64 (/.f64 M 2) (/.f64 D d))
3.5b	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
7.6b	(.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))

rewrite341.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

3.9b

Rules

210×	`add-exp-log_binary64_1139`
121×	`prod-exp_binary64_1150`
47×	`add-sqr-sqrt_binary64_1123`
43×	`div-exp_binary64_1152`
40×	`times-frac_binary64_1107`
36×	`associate-r_binary64_1041`
33×	`add-cbrt-cube_binary64_1137` `add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
30×	`pow-exp_binary64_1169`
20×	`associate-l_binary64_1042`
19×	`cbrt-unprod_binary64_1134`
9×	`pow1_binary64_1162` `cbrt-prod_binary64_1132`
7×	`cbrt-undiv_binary64_1135` `unswap-sqr_binary64_1069`
6×	`pow-to-exp_binary64_1170`
4×	`add-log-exp_binary64_1140`
3×	`pow-prod-down_binary64_1172` `div-inv_binary64_1098` `*-commutative_binary64_1032` `sqrt-prod_binary64_1117`
2×	`associate-*r/_binary64_1043` `sqrt-div_binary64_1118` `unpow2_binary64_1166` `sqr-pow_binary64_1073`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114` `pow2_binary64_1182` `unpow-prod-down_binary64_1180` `frac-times_binary64_1111` `associate-*l/_binary64_1044`

Counts

4 → 169

Calls

4 calls:

17.0ms	(.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
16.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
10.0ms	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))

Compiler

Compiled 5964 to 2724 computations (54.3% saved)

series1.7s (7%)

Error

3.2b

Counts

4 → 51

Calls

4 calls:

691.0ms	(.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
598.0ms	(.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
256.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
135.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

Compiler

Compiled 3582 to 3102 computations (13.4% saved)

simplify143.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

542×	`associate-l_binary64_1042`
372×	`associate-r_binary64_1041`
257×	`associate-r/_binary64_1043` `-commutative_binary64_1032`
247×	`unswap-sqr_binary64_1069`
236×	`associate-/l*_binary64_1046`
174×	`associate-*l/_binary64_1044`
163×	`cancel-sign-sub-inv_binary64_1067`
138×	`times-frac_binary64_1107`
112×	`log-prod_binary64_1187`
94×	`swap-sqr_binary64_1068`
91×	`exp-prod_binary64_1153`
86×	`associate-/r*_binary64_1045`
83×	`cube-prod_binary64_1129`
76×	`sqr-pow_binary64_1073`
55×	`associate-/l/_binary64_1048`
48×	`neg-sub0_binary64_1096`
47×	`*-lft-identity_binary64_1090`
46×	`log-div_binary64_1188` `*-rgt-identity_binary64_1091`
42×	`neg-mul-1_binary64_1097`
41×	`+-commutative_binary64_1031`
37×	`associate-+l+_binary64_1034`
33×	`sub-neg_binary64_1094`
31×	`distribute-rgt-neg-in_binary64_1059`
25×	`distribute-lft-neg-in_binary64_1058`
24×	`cube-div_binary64_1130`
19×	`associate-/r/_binary64_1047`
17×	`associate-+r-_binary64_1035`
13×	`/-rgt-identity_binary64_1092` `associate-+r+_binary64_1033`
12×	`distribute-neg-frac_binary64_1065`
10×	`exp-sqrt_binary64_1154` `rem-sqrt-square_binary64_1114`
9×	`pow-plus_binary64_1164`
8×	`log-pow_binary64_1190` `mul-1-neg_binary64_1093`
7×	`unpow3_binary64_1167` `unpow2_binary64_1166` `unpow1/2_binary64_1165` `unpow1_binary64_1159` `cube-unmult_binary64_1138` `pow-sqr_binary64_1074`
5×	`cube-mult_binary64_1131` `associate-+l-_binary64_1036`
4×	`distribute-lft-out_binary64_1052`
3×	`distribute-rgt-out_binary64_1054` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`
2×	`distribute-lft-neg-out_binary64_1060` `distribute-rgt1-in_binary64_1057`
1×	`unpow1/3_binary64_1168` `1-exp_binary64_1145` `exp-1-e_binary64_1144` `rem-3cbrt-rft_binary64_1127` `rem-3cbrt-lft_binary64_1126` `rem-cbrt-cube_binary64_1125` `rem-cube-cbrt_binary64_1124` `rem-square-sqrt_binary64_1113` `count-2_binary64_1049` `associate--r-_binary64_1040` `associate--r+_binary64_1037`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1364` `erf-erfc_binary64_1363` `erf-odd_binary64_1362` `if-if-and-not_binary64_1361` `if-if-and_binary64_1360` `if-if-or-not_binary64_1359` `if-if-or_binary64_1358` `if-not_binary64_1357` `if-same_binary64_1356` `if-false_binary64_1355` `if-true_binary64_1354` `not-gte_binary64_1353` `not-lte_binary64_1352` `not-gt_binary64_1351` `not-lt_binary64_1350` `gte-same_binary64_1349` `lte-same_binary64_1348` `gt-same_binary64_1347` `lt-same_binary64_1346` `sinh---cosh_binary64_1293` `sinh-+-cosh_binary64_1292` `sinh-cosh_binary64_1291` `tanh-def-c_binary64_1290` `tanh-def-b_binary64_1289` `tanh-def-a_binary64_1288` `cosh-def_binary64_1287` `sinh-def_binary64_1286` `tan-neg_binary64_1233` `cos-neg_binary64_1232` `sin-neg_binary64_1231` `tan-0_binary64_1230` `cos-0_binary64_1229` `sin-0_binary64_1228` `hang-m-tan_binary64_1227` `hang-p-tan_binary64_1226` `hang-m0-tan_binary64_1225` `hang-p0-tan_binary64_1224` `hang-0m-tan_binary64_1223` `hang-0p-tan_binary64_1222` `tan-+PI/2_binary64_1221` `tan-+PI_binary64_1220` `tan-PI_binary64_1219` `tan-PI/3_binary64_1218` `tan-PI/4_binary64_1217` `tan-PI/6_binary64_1216` `cos-+PI/2_binary64_1215` `cos-+PI_binary64_1214` `cos-PI_binary64_1213` `cos-PI/2_binary64_1212` `cos-PI/3_binary64_1211` `cos-PI/4_binary64_1210` `cos-PI/6_binary64_1209` `sin-+PI/2_binary64_1208` `sin-+PI_binary64_1207` `sin-PI_binary64_1206` `sin-PI/2_binary64_1205` `sin-PI/3_binary64_1204` `sin-PI/4_binary64_1203` `sin-PI/6_binary64_1202` `sub-1-sin_binary64_1201` `sub-1-cos_binary64_1200` `-1-add-sin_binary64_1199` `-1-add-cos_binary64_1198` `1-sub-sin_binary64_1197` `1-sub-cos_binary64_1196` `cos-sin-sum_binary64_1195` `log-E_binary64_1191` `log-rec_binary64_1189` `pow-base-0_binary64_1185` `exp-to-pow_binary64_1163` `pow-base-1_binary64_1161` `unpow0_binary64_1160` `unpow-1_binary64_1158` `exp-lft-cube_binary64_1157` `exp-lft-sqr_binary64_1156` `exp-cbrt_binary64_1155` `div-exp_binary64_1152` `rec-exp_binary64_1151` `prod-exp_binary64_1150` `exp-diff_binary64_1149` `exp-neg_binary64_1148` `exp-sum_binary64_1147` `e-exp-1_binary64_1146` `exp-0_binary64_1143` `rem-log-exp_binary64_1142` `rem-exp-log_binary64_1141` `cube-neg_binary64_1128` `sqr-abs_binary64_1116` `sqr-neg_binary64_1115` `div-sub_binary64_1106` `unsub-neg_binary64_1095` `remove-double-neg_binary64_1089` `sub0-neg_binary64_1088` `--rgt-identity_binary64_1087` `+-rgt-identity_binary64_1086` `+-lft-identity_binary64_1085` `mul0-rgt_binary64_1084` `mul0-lft_binary64_1083` `div0_binary64_1082` `*-inverses_binary64_1081` `+-inverses_binary64_1080` `lft-mult-inverse_binary64_1079` `rgt-mult-inverse_binary64_1078` `remove-double-div_binary64_1077` `difference-of-sqr--1_binary64_1072` `difference-of-sqr-1_binary64_1071` `difference-of-squares_binary64_1070` `cancel-sign-sub_binary64_1066` `distribute-frac-neg_binary64_1064` `distribute-neg-out_binary64_1063` `distribute-neg-in_binary64_1062` `distribute-rgt-neg-out_binary64_1061` `distribute-lft1-in_binary64_1056` `distribute-rgt-out--_binary64_1055` `distribute-lft-out--_binary64_1053` `associate--l-_binary64_1039` `associate--l+_binary64_1038`

Counts

220 → 647

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	355	5743
1	890	4672
2	3649	4504

prune1.5s (6.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	643	4	647
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	645	17	662

Error

3.6b

Counts

662 → 17

Compiler

Compiled 21340 to 9980 computations (53.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.1b	(.f64 (pow.f64 (/.f64 (.f64 M (/.f64 D d)) 2) 2) (cbrt.f64 h))
3.1b	(*.f64 M (/.f64 D d))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M (/.f64 D d)) 2) 2) (cbrt.f64 h)) (cbrt.f64 h)) (/.f64 (cbrt.f64 h) l))))
7.6b	(.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M (/.f64 D d)) 2) 2) (cbrt.f64 h)) (cbrt.f64 h)) (/.f64 (cbrt.f64 h) l))

rewrite277.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

3.6b

Rules

102×	`add-exp-log_binary64_1139`
56×	`prod-exp_binary64_1150`
49×	`add-sqr-sqrt_binary64_1123`
41×	`associate-r_binary64_1041`
31×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101` `times-frac_binary64_1107`
22×	`add-cbrt-cube_binary64_1137`
21×	`div-exp_binary64_1152`
16×	`associate-l_binary64_1042` `cbrt-prod_binary64_1132`
15×	`cbrt-unprod_binary64_1134`
12×	`pow1_binary64_1162` `pow-exp_binary64_1169`
10×	`unswap-sqr_binary64_1069`
9×	`unpow-prod-down_binary64_1180`
4×	`pow-prod-down_binary64_1172` `add-log-exp_binary64_1140` `cbrt-undiv_binary64_1135`
3×	`pow-to-exp_binary64_1170` `div-inv_binary64_1098` `*-commutative_binary64_1032` `sqrt-prod_binary64_1117` `unpow2_binary64_1166` `sqr-pow_binary64_1073`
2×	`associate-*r/_binary64_1043` `sqrt-div_binary64_1118`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114`

Counts

4 → 144

Calls

4 calls:

20.0ms	(.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M (/.f64 D d)) 2) 2) (cbrt.f64 h)) (cbrt.f64 h)) (/.f64 (cbrt.f64 h) l))
10.0ms	(.f64 (pow.f64 (/.f64 (.f64 M (/.f64 D d)) 2) 2) (cbrt.f64 h))
8.0ms	(*.f64 M (/.f64 D d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M (/.f64 D d)) 2) 2) (cbrt.f64 h)) (cbrt.f64 h)) (/.f64 (cbrt.f64 h) l))))

Compiler

Compiled 5162 to 2349 computations (54.5% saved)

series1.6s (6.6%)

Error

2.9b

Counts

4 → 51

Calls

4 calls:

626.0ms	(.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M (/.f64 D d)) 2) 2) (cbrt.f64 h)) (cbrt.f64 h)) (/.f64 (cbrt.f64 h) l))
582.0ms	(.f64 (pow.f64 (/.f64 (.f64 M (/.f64 D d)) 2) 2) (cbrt.f64 h))
251.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M (/.f64 D d)) 2) 2) (cbrt.f64 h)) (cbrt.f64 h)) (/.f64 (cbrt.f64 h) l))))
113.0ms	(*.f64 M (/.f64 D d))

Compiler

Compiled 3618 to 3074 computations (15% saved)

simplify126.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

518×	`associate-l_binary64_1042`
365×	`associate-r_binary64_1041`
263×	`unswap-sqr_binary64_1069`
238×	`distribute-rgt-neg-in_binary64_1059`
231×	`*-commutative_binary64_1032`
199×	`associate-/l*_binary64_1046`
192×	`associate-*r/_binary64_1043`
137×	`times-frac_binary64_1107`
130×	`cancel-sign-sub-inv_binary64_1067`
116×	`associate-*l/_binary64_1044`
95×	`distribute-neg-frac_binary64_1065`
87×	`associate-/r*_binary64_1045`
85×	`log-prod_binary64_1187`
81×	`sqr-pow_binary64_1073`
73×	`cube-prod_binary64_1129`
64×	`exp-prod_binary64_1153`
49×	`-rgt-identity_binary64_1091` `-lft-identity_binary64_1090` `associate-/l/_binary64_1048`
48×	`neg-sub0_binary64_1096`
41×	`neg-mul-1_binary64_1097`
39×	`swap-sqr_binary64_1068`
37×	`sub-neg_binary64_1094` `+-commutative_binary64_1031`
29×	`associate-+l+_binary64_1034`
27×	`log-div_binary64_1188`
25×	`distribute-lft-neg-in_binary64_1058`
20×	`associate-/r/_binary64_1047`
17×	`cube-div_binary64_1130`
15×	`/-rgt-identity_binary64_1092`
12×	`distribute-lft-neg-out_binary64_1060`
11×	`log-pow_binary64_1190`
10×	`cube-unmult_binary64_1138` `rem-sqrt-square_binary64_1114`
9×	`unpow2_binary64_1166` `unpow1/2_binary64_1165` `unpow1_binary64_1159` `distribute-rgt-neg-out_binary64_1061` `associate-+r-_binary64_1035`
8×	`unpow3_binary64_1167` `pow-plus_binary64_1164` `mul-1-neg_binary64_1093`
7×	`pow-sqr_binary64_1074` `distribute-frac-neg_binary64_1064` `associate-+r+_binary64_1033`
5×	`cube-mult_binary64_1131`
4×	`associate--l+_binary64_1038`
3×	`exp-sqrt_binary64_1154` `distribute-rgt-out_binary64_1054` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050` `associate-+l-_binary64_1036`
2×	`log-rec_binary64_1189` `unpow1/3_binary64_1168` `rem-square-sqrt_binary64_1113` `distribute-rgt1-in_binary64_1057` `distribute-lft-out_binary64_1052` `associate--l-_binary64_1039`
1×	`1-exp_binary64_1145` `exp-1-e_binary64_1144` `rem-3cbrt-rft_binary64_1127` `rem-cube-cbrt_binary64_1124` `unsub-neg_binary64_1095` `count-2_binary64_1049`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1364` `erf-erfc_binary64_1363` `erf-odd_binary64_1362` `if-if-and-not_binary64_1361` `if-if-and_binary64_1360` `if-if-or-not_binary64_1359` `if-if-or_binary64_1358` `if-not_binary64_1357` `if-same_binary64_1356` `if-false_binary64_1355` `if-true_binary64_1354` `not-gte_binary64_1353` `not-lte_binary64_1352` `not-gt_binary64_1351` `not-lt_binary64_1350` `gte-same_binary64_1349` `lte-same_binary64_1348` `gt-same_binary64_1347` `lt-same_binary64_1346` `sinh---cosh_binary64_1293` `sinh-+-cosh_binary64_1292` `sinh-cosh_binary64_1291` `tanh-def-c_binary64_1290` `tanh-def-b_binary64_1289` `tanh-def-a_binary64_1288` `cosh-def_binary64_1287` `sinh-def_binary64_1286` `tan-neg_binary64_1233` `cos-neg_binary64_1232` `sin-neg_binary64_1231` `tan-0_binary64_1230` `cos-0_binary64_1229` `sin-0_binary64_1228` `hang-m-tan_binary64_1227` `hang-p-tan_binary64_1226` `hang-m0-tan_binary64_1225` `hang-p0-tan_binary64_1224` `hang-0m-tan_binary64_1223` `hang-0p-tan_binary64_1222` `tan-+PI/2_binary64_1221` `tan-+PI_binary64_1220` `tan-PI_binary64_1219` `tan-PI/3_binary64_1218` `tan-PI/4_binary64_1217` `tan-PI/6_binary64_1216` `cos-+PI/2_binary64_1215` `cos-+PI_binary64_1214` `cos-PI_binary64_1213` `cos-PI/2_binary64_1212` `cos-PI/3_binary64_1211` `cos-PI/4_binary64_1210` `cos-PI/6_binary64_1209` `sin-+PI/2_binary64_1208` `sin-+PI_binary64_1207` `sin-PI_binary64_1206` `sin-PI/2_binary64_1205` `sin-PI/3_binary64_1204` `sin-PI/4_binary64_1203` `sin-PI/6_binary64_1202` `sub-1-sin_binary64_1201` `sub-1-cos_binary64_1200` `-1-add-sin_binary64_1199` `-1-add-cos_binary64_1198` `1-sub-sin_binary64_1197` `1-sub-cos_binary64_1196` `cos-sin-sum_binary64_1195` `log-E_binary64_1191` `pow-base-0_binary64_1185` `exp-to-pow_binary64_1163` `pow-base-1_binary64_1161` `unpow0_binary64_1160` `unpow-1_binary64_1158` `exp-lft-cube_binary64_1157` `exp-lft-sqr_binary64_1156` `exp-cbrt_binary64_1155` `div-exp_binary64_1152` `rec-exp_binary64_1151` `prod-exp_binary64_1150` `exp-diff_binary64_1149` `exp-neg_binary64_1148` `exp-sum_binary64_1147` `e-exp-1_binary64_1146` `exp-0_binary64_1143` `rem-log-exp_binary64_1142` `rem-exp-log_binary64_1141` `cube-neg_binary64_1128` `rem-3cbrt-lft_binary64_1126` `rem-cbrt-cube_binary64_1125` `sqr-abs_binary64_1116` `sqr-neg_binary64_1115` `div-sub_binary64_1106` `remove-double-neg_binary64_1089` `sub0-neg_binary64_1088` `--rgt-identity_binary64_1087` `+-rgt-identity_binary64_1086` `+-lft-identity_binary64_1085` `mul0-rgt_binary64_1084` `mul0-lft_binary64_1083` `div0_binary64_1082` `*-inverses_binary64_1081` `+-inverses_binary64_1080` `lft-mult-inverse_binary64_1079` `rgt-mult-inverse_binary64_1078` `remove-double-div_binary64_1077` `difference-of-sqr--1_binary64_1072` `difference-of-sqr-1_binary64_1071` `difference-of-squares_binary64_1070` `cancel-sign-sub_binary64_1066` `distribute-neg-out_binary64_1063` `distribute-neg-in_binary64_1062` `distribute-lft1-in_binary64_1056` `distribute-rgt-out--_binary64_1055` `distribute-lft-out--_binary64_1053` `associate--r-_binary64_1040` `associate--r+_binary64_1037`

Counts

195 → 658

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	332	4943
1	814	4408
2	3562	3986

prune1.5s (6.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	655	3	658
Fresh	4	12	16
Picked	0	1	1
Done	0	0	0
Total	659	16	675

Error

2.9b

Counts

675 → 16

Compiler

Compiled 23666 to 11629 computations (50.9% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 (/.f64 D d) (/.f64 2 M)) 2)) l)))
4.4b	(/.f64 (*.f64 h (pow.f64 (/.f64 (/.f64 D d) (/.f64 2 M)) 2)) l)
5.2b	(*.f64 h (pow.f64 (/.f64 (/.f64 D d) (/.f64 2 M)) 2))
5.3b	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 (/.f64 D d) (/.f64 2 M)) 2)) l))) 3))

rewrite865.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

2.0b

Rules

414×	`times-frac_binary64_1107`
229×	`add-sqr-sqrt_binary64_1123`
206×	`*-un-lft-identity_binary64_1101`
197×	`add-cube-cbrt_binary64_1136`
188×	`unpow-prod-down_binary64_1180`
179×	`associate-r_binary64_1041`
55×	`add-exp-log_binary64_1139`
28×	`div-inv_binary64_1098`
24×	`cbrt-prod_binary64_1132` `div-exp_binary64_1152`
18×	`sqrt-prod_binary64_1117`
14×	`prod-exp_binary64_1150`
11×	`add-cbrt-cube_binary64_1137`
10×	`pow-exp_binary64_1169`
9×	`cube-prod_binary64_1129`
8×	`unswap-sqr_binary64_1069`
6×	`difference-of-squares_binary64_1070`
5×	`pow1_binary64_1162`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
3×	`distribute-lft-out--_binary64_1053` `sqr-pow_binary64_1073` `associate-l_binary64_1042` `associate-/r*_binary64_1045`
2×	`flip3--_binary64_1105` `cube-div_binary64_1130` `cbrt-div_binary64_1133` `flip--_binary64_1076` `pow-to-exp_binary64_1170` `cbrt-unprod_binary64_1134` `unpow2_binary64_1166` `cbrt-undiv_binary64_1135`
1×	`pow1/3_binary64_1183` `unpow3_binary64_1167` `cube-mult_binary64_1131` `rem-cbrt-cube_binary64_1125` `associate-/r/_binary64_1047` `-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114`

Counts

4 → 286

Calls

4 calls:

71.0ms	(*.f64 h (pow.f64 (/.f64 (/.f64 D d) (/.f64 2 M)) 2))
37.0ms	(/.f64 (*.f64 h (pow.f64 (/.f64 (/.f64 D d) (/.f64 2 M)) 2)) l)
9.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 (/.f64 D d) (/.f64 2 M)) 2)) l))) 3))
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 (/.f64 D d) (/.f64 2 M)) 2)) l)))

Compiler

Compiled 10536 to 6695 computations (36.5% saved)

series1.4s (5.7%)

Error

2.9b

Counts

4 → 57

Calls

4 calls:

542.0ms	(/.f64 (*.f64 h (pow.f64 (/.f64 (/.f64 D d) (/.f64 2 M)) 2)) l)
360.0ms	(*.f64 h (pow.f64 (/.f64 (/.f64 D d) (/.f64 2 M)) 2))
232.0ms	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 (/.f64 D d) (/.f64 2 M)) 2)) l)))
230.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 (/.f64 D d) (/.f64 2 M)) 2)) l))) 3))

Compiler

Compiled 3806 to 3525 computations (7.4% saved)

simplify144.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

628×	`associate-*l/_binary64_1044`
372×	`associate-*r/_binary64_1043`
329×	`sqr-pow_binary64_1073`
327×	`associate-/l/_binary64_1048`
213×	`associate-/r/_binary64_1047`
194×	`associate-/l*_binary64_1046`
188×	`associate-/r*_binary64_1045`
187×	`*-commutative_binary64_1032`
150×	`unpow2_binary64_1166`
149×	`unpow1_binary64_1159`
146×	`times-frac_binary64_1107`
103×	`swap-sqr_binary64_1068`
25×	`sub-neg_binary64_1094`
23×	`distribute-rgt-neg-in_binary64_1059`
20×	`neg-sub0_binary64_1096` `distribute-neg-frac_binary64_1065`
18×	`neg-mul-1_binary64_1097` `distribute-lft-neg-in_binary64_1058`
17×	`/-rgt-identity_binary64_1092`
15×	`unpow3_binary64_1167`
14×	`unswap-sqr_binary64_1069`
13×	`cube-mult_binary64_1131` `rem-square-sqrt_binary64_1113`
12×	`rem-cbrt-cube_binary64_1125`
11×	`log-div_binary64_1188` `log-prod_binary64_1187` `*-rgt-identity_binary64_1091`
10×	`+-commutative_binary64_1031`
9×	`exp-prod_binary64_1153` `cancel-sign-sub-inv_binary64_1067` `associate-r_binary64_1041`
8×	`rem-sqrt-square_binary64_1114`
7×	`associate-l_binary64_1042`
6×	`cube-div_binary64_1130` `associate--l+_binary64_1038`
5×	`cube-prod_binary64_1129`
4×	`mul-1-neg_binary64_1093` `*-lft-identity_binary64_1090`
3×	`log-pow_binary64_1190` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`
2×	`cube-unmult_binary64_1138` `remove-double-div_binary64_1077` `pow-sqr_binary64_1074` `distribute-rgt1-in_binary64_1057`
1×	`unpow1/2_binary64_1165` `1-exp_binary64_1145` `rem-3cbrt-lft_binary64_1126` `rem-cube-cbrt_binary64_1124` `sqr-abs_binary64_1116` `distribute-neg-in_binary64_1062` `distribute-lft-neg-out_binary64_1060` `distribute-rgt-out_binary64_1054` `associate--r-_binary64_1040` `associate--l-_binary64_1039` `associate-+r+_binary64_1033`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1364` `erf-erfc_binary64_1363` `erf-odd_binary64_1362` `if-if-and-not_binary64_1361` `if-if-and_binary64_1360` `if-if-or-not_binary64_1359` `if-if-or_binary64_1358` `if-not_binary64_1357` `if-same_binary64_1356` `if-false_binary64_1355` `if-true_binary64_1354` `not-gte_binary64_1353` `not-lte_binary64_1352` `not-gt_binary64_1351` `not-lt_binary64_1350` `gte-same_binary64_1349` `lte-same_binary64_1348` `gt-same_binary64_1347` `lt-same_binary64_1346` `sinh---cosh_binary64_1293` `sinh-+-cosh_binary64_1292` `sinh-cosh_binary64_1291` `tanh-def-c_binary64_1290` `tanh-def-b_binary64_1289` `tanh-def-a_binary64_1288` `cosh-def_binary64_1287` `sinh-def_binary64_1286` `tan-neg_binary64_1233` `cos-neg_binary64_1232` `sin-neg_binary64_1231` `tan-0_binary64_1230` `cos-0_binary64_1229` `sin-0_binary64_1228` `hang-m-tan_binary64_1227` `hang-p-tan_binary64_1226` `hang-m0-tan_binary64_1225` `hang-p0-tan_binary64_1224` `hang-0m-tan_binary64_1223` `hang-0p-tan_binary64_1222` `tan-+PI/2_binary64_1221` `tan-+PI_binary64_1220` `tan-PI_binary64_1219` `tan-PI/3_binary64_1218` `tan-PI/4_binary64_1217` `tan-PI/6_binary64_1216` `cos-+PI/2_binary64_1215` `cos-+PI_binary64_1214` `cos-PI_binary64_1213` `cos-PI/2_binary64_1212` `cos-PI/3_binary64_1211` `cos-PI/4_binary64_1210` `cos-PI/6_binary64_1209` `sin-+PI/2_binary64_1208` `sin-+PI_binary64_1207` `sin-PI_binary64_1206` `sin-PI/2_binary64_1205` `sin-PI/3_binary64_1204` `sin-PI/4_binary64_1203` `sin-PI/6_binary64_1202` `sub-1-sin_binary64_1201` `sub-1-cos_binary64_1200` `-1-add-sin_binary64_1199` `-1-add-cos_binary64_1198` `1-sub-sin_binary64_1197` `1-sub-cos_binary64_1196` `cos-sin-sum_binary64_1195` `log-E_binary64_1191` `log-rec_binary64_1189` `pow-base-0_binary64_1185` `unpow1/3_binary64_1168` `pow-plus_binary64_1164` `exp-to-pow_binary64_1163` `pow-base-1_binary64_1161` `unpow0_binary64_1160` `unpow-1_binary64_1158` `exp-lft-cube_binary64_1157` `exp-lft-sqr_binary64_1156` `exp-cbrt_binary64_1155` `exp-sqrt_binary64_1154` `div-exp_binary64_1152` `rec-exp_binary64_1151` `prod-exp_binary64_1150` `exp-diff_binary64_1149` `exp-neg_binary64_1148` `exp-sum_binary64_1147` `e-exp-1_binary64_1146` `exp-1-e_binary64_1144` `exp-0_binary64_1143` `rem-log-exp_binary64_1142` `rem-exp-log_binary64_1141` `cube-neg_binary64_1128` `rem-3cbrt-rft_binary64_1127` `sqr-neg_binary64_1115` `div-sub_binary64_1106` `unsub-neg_binary64_1095` `remove-double-neg_binary64_1089` `sub0-neg_binary64_1088` `--rgt-identity_binary64_1087` `+-rgt-identity_binary64_1086` `+-lft-identity_binary64_1085` `mul0-rgt_binary64_1084` `mul0-lft_binary64_1083` `div0_binary64_1082` `*-inverses_binary64_1081` `+-inverses_binary64_1080` `lft-mult-inverse_binary64_1079` `rgt-mult-inverse_binary64_1078` `difference-of-sqr--1_binary64_1072` `difference-of-sqr-1_binary64_1071` `difference-of-squares_binary64_1070` `cancel-sign-sub_binary64_1066` `distribute-frac-neg_binary64_1064` `distribute-neg-out_binary64_1063` `distribute-rgt-neg-out_binary64_1061` `distribute-lft1-in_binary64_1056` `distribute-rgt-out--_binary64_1055` `distribute-lft-out--_binary64_1053` `distribute-lft-out_binary64_1052` `count-2_binary64_1049` `associate--r+_binary64_1037` `associate-+l-_binary64_1036` `associate-+r-_binary64_1035` `associate-+l+_binary64_1034`

Counts

343 → 756

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	696	8325
1	1831	8009

prune2.3s (9.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	752	4	756
Fresh	2	12	14
Picked	1	0	1
Done	0	1	1
Total	755	17	772

Error

2.0b

Counts

772 → 17

Compiler

Compiled 26478 to 16547 computations (37.5% saved)

regimes3.9s (15.8%)

Accuracy

Total 5.4b remaining (62.3%)

Threshold costs 0b (0%)

Compiler

Compiled 45446 to 40955 computations (9.9% saved)

bsearch6.0ms (0%)

Compiler: Compiled 9 to 12 computations (-33.3% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative_binary64_1032`
19×	`sub-neg_binary64_1094` `+-commutative_binary64_1031`
16×	`neg-mul-1_binary64_1097` `neg-sub0_binary64_1096`
14×	`distribute-rgt-neg-in_binary64_1059`
12×	`distribute-lft-neg-in_binary64_1058`
5×	`distribute-neg-frac_binary64_1065`
4×	`cancel-sign-sub-inv_binary64_1067`
2×	`distribute-lft-neg-out_binary64_1060`
1×	`1-exp_binary64_1145`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64_1361` `if-if-and_binary64_1360` `if-if-or-not_binary64_1359` `if-if-or_binary64_1358` `if-not_binary64_1357` `if-same_binary64_1356` `if-false_binary64_1355` `if-true_binary64_1354` `tan-0_binary64_1230` `cos-0_binary64_1229` `sin-0_binary64_1228` `unpow1_binary64_1159` `e-exp-1_binary64_1146` `exp-1-e_binary64_1144` `exp-0_binary64_1143` `sqr-abs_binary64_1116` `sqr-neg_binary64_1115` `unsub-neg_binary64_1095` `mul-1-neg_binary64_1093` `/-rgt-identity_binary64_1092` `-rgt-identity_binary64_1091` `-lft-identity_binary64_1090` `remove-double-neg_binary64_1089` `sub0-neg_binary64_1088` `--rgt-identity_binary64_1087` `+-rgt-identity_binary64_1086` `+-lft-identity_binary64_1085` `cancel-sign-sub_binary64_1066` `distribute-frac-neg_binary64_1064` `distribute-neg-out_binary64_1063` `distribute-neg-in_binary64_1062` `distribute-rgt-neg-out_binary64_1061`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	140
1	71	140
2	99	140
3	136	140
4	172	140
5	189	140
6	195	140

Proof

(if real (<= f64 (pow f64 (/ f64 (* f64 h0 h1) (* f64 2 h2)) 2) 8070487952650597/15829145694278690179872161345257420162248406342477557754500035589945422406818039498900249667919554879334250971265032917718487362195632077437922953926521162746662833417516744704) (* f64 h3 (cbrt f64 (pow f64 (sqrt f64 (- f64 1 (/ f64 (=> (* f64 (* f64 h4 (/ f64 (/ f64 h1 h2) (/ f64 2 h0))) (/ f64 (/ f64 h1 h2) (/ f64 2 h0)))) h5))) 3))) (if real (<= f64 (pow f64 (/ f64 (* f64 h0 h1) (* f64 2 h2)) 2) 794401870418910368310417058011242561964038864083915166020888245105612236397422984065112225594544125874425781998274445691753823339309677128710142162850982087131743112048903598878009597092788307041657438925976288807995714463443951078537523582252158545586814976) (* f64 h3 (sqrt f64 (- f64 1 (* f64 (pow f64 (/ f64 (* f64 h0 h1) (* f64 2 h2)) 2) (/ f64 h4 h5))))) (* f64 h3 (sqrt f64 (- f64 1 (* f64 (* f64 (/ f64 h0 2) (/ f64 h1 h2)) (* f64 (/ f64 h0 2) (* f64 (/ f64 h1 h2) (/ f64 h4 h5)))))))))
*-commutative_binary64_1032 =>
(if real (<= f64 (pow f64 (/ f64 (* f64 h0 h1) (* f64 2 h2)) 2) 8070487952650597/15829145694278690179872161345257420162248406342477557754500035589945422406818039498900249667919554879334250971265032917718487362195632077437922953926521162746662833417516744704) (* f64 h3 (cbrt f64 (pow f64 (sqrt f64 (- f64 1 (/ f64 (* f64 (/ f64 (/ f64 h1 h2) (/ f64 2 h0)) (* f64 h4 (/ f64 (/ f64 h1 h2) (/ f64 2 h0)))) h5))) 3))) (if real (<= f64 (pow f64 (/ f64 (* f64 h0 h1) (* f64 2 h2)) 2) 794401870418910368310417058011242561964038864083915166020888245105612236397422984065112225594544125874425781998274445691753823339309677128710142162850982087131743112048903598878009597092788307041657438925976288807995714463443951078537523582252158545586814976) (* f64 h3 (sqrt f64 (- f64 1 (* f64 (pow f64 (/ f64 (* f64 h0 h1) (* f64 2 h2)) 2) (/ f64 h4 h5))))) (* f64 h3 (sqrt f64 (- f64 1 (* f64 (=> (* f64 (/ f64 h0 2) (/ f64 h1 h2))) (* f64 (/ f64 h0 2) (* f64 (/ f64 h1 h2) (/ f64 h4 h5)))))))))
*-commutative_binary64_1032 =>
(if real (<= f64 (pow f64 (/ f64 (* f64 h0 h1) (* f64 2 h2)) 2) 8070487952650597/15829145694278690179872161345257420162248406342477557754500035589945422406818039498900249667919554879334250971265032917718487362195632077437922953926521162746662833417516744704) (* f64 h3 (cbrt f64 (pow f64 (sqrt f64 (- f64 1 (/ f64 (* f64 (/ f64 (/ f64 h1 h2) (/ f64 2 h0)) (* f64 h4 (/ f64 (/ f64 h1 h2) (/ f64 2 h0)))) h5))) 3))) (if real (<= f64 (pow f64 (/ f64 (* f64 h0 h1) (* f64 2 h2)) 2) 794401870418910368310417058011242561964038864083915166020888245105612236397422984065112225594544125874425781998274445691753823339309677128710142162850982087131743112048903598878009597092788307041657438925976288807995714463443951078537523582252158545586814976) (* f64 h3 (sqrt f64 (- f64 1 (* f64 (pow f64 (/ f64 (* f64 h0 h1) (* f64 2 h2)) 2) (/ f64 h4 h5))))) (* f64 h3 (sqrt f64 (- f64 1 (* f64 (* f64 (/ f64 h1 h2) (/ f64 h0 2)) (* f64 (/ f64 h0 2) (* f64 (/ f64 h1 h2) (/ f64 h4 h5)))))))))

end0.0ms (0%)

sample4.1s (16.7%)

Algorithm

1×

intervals

Results

602.0ms	8000×	body	128	valid
219.0ms	3063×	body	128	nan
96.0ms	1248×	body	128	invalid

Compiler

Compiled 3024 to 2687 computations (11.1% saved)

Details

analyze2.1s (8.6%)

sample57.0ms (0.2%)

simplify130.0ms (0.5%)

prune12.0ms (0%)

localize15.0ms (0.1%)

rewrite286.0ms (1.1%)

series1.5s (5.9%)

simplify117.0ms (0.5%)

prune443.0ms (1.8%)

localize19.0ms (0.1%)

rewrite341.0ms (1.4%)

series1.7s (7%)

simplify143.0ms (0.6%)

prune1.5s (6.2%)

localize19.0ms (0.1%)

rewrite277.0ms (1.1%)

series1.6s (6.6%)

simplify126.0ms (0.5%)

prune1.5s (6.2%)

localize20.0ms (0.1%)

rewrite865.0ms (3.5%)

series1.4s (5.7%)

simplify144.0ms (0.6%)

prune2.3s (9.2%)

regimes3.9s (15.8%)

bsearch6.0ms (0%)

simplify14.0ms (0.1%)

end0.0ms (0%)

sample4.1s (16.7%)

Profiling