Details

analyze2.0s (6.1%)

Algorithm

1×	search
2×	egg-herbie

Rules

752×	`associate-*r/_binary64_1043`
481×	`*-commutative_binary64_1032`
271×	`cancel-sign-sub-inv_binary64_1067`
230×	`associate-/l*_binary64_1046`
224×	`neg-mul-1_binary64_1097` `neg-sub0_binary64_1096`
216×	`unswap-sqr_binary64_1069`
205×	`distribute-rgt-neg-in_binary64_1059`
185×	`distribute-lft-neg-in_binary64_1058`
140×	`distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`
129×	`associate-l_binary64_1042`
118×	`associate-/r/_binary64_1047`
100×	`swap-sqr_binary64_1068`
94×	`distribute-neg-frac_binary64_1065`
87×	`sub-neg_binary64_1094`
85×	`sqr-pow_binary64_1073`
77×	`associate-r_binary64_1041`
72×	`times-frac_binary64_1107`
71×	`associate-/r*_binary64_1045`
48×	`associate-*l/_binary64_1044`
40×	`unsub-neg_binary64_1095` `distribute-lft-neg-out_binary64_1060`
29×	`-rgt-identity_binary64_1091` `-lft-identity_binary64_1090`
21×	`unpow1/2_binary64_1165`
20×	`div-sub_binary64_1106` `distribute-rgt-neg-out_binary64_1061`
18×	`associate-/l/_binary64_1048`
10×	`unpow2_binary64_1166` `sub0-neg_binary64_1088` `associate-+l-_binary64_1036` `+-commutative_binary64_1031`
9×	`unpow1_binary64_1159` `rem-sqrt-square_binary64_1114`
1×	`1-exp_binary64_1145` `swap-M-D`
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` `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` `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-unmult_binary64_1138` `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` `remove-double-neg_binary64_1089` `--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` `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-frac-neg_binary64_1064` `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-+l+_binary64_1034` `associate-+r+_binary64_1033`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	122	451
1	393	451
2	1448	451
3	4121	451
4	5362	451
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Symmetry

(sort M D)

Compiler

Compiled 36 to 32 computations (11.1% saved)

sample150.0ms (0.5%)

Algorithm

1×

intervals

Results

39.0ms	256×	body	128	valid
33.0ms	276×	body	128	nan
23.0ms	164×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify39.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

679×	`distribute-neg-frac_binary64_1065`
437×	`*-commutative_binary64_1032`
425×	`associate-/l*_binary64_1046`
347×	`cancel-sign-sub-inv_binary64_1067`
263×	`associate-/l/_binary64_1048`
212×	`associate-/r/_binary64_1047`
203×	`associate-/r*_binary64_1045`
201×	`neg-sub0_binary64_1096`
200×	`neg-mul-1_binary64_1097`
198×	`distribute-rgt-neg-in_binary64_1059`
195×	`distribute-lft-neg-in_binary64_1058`
188×	`times-frac_binary64_1107`
160×	`associate-l_binary64_1042`
141×	`associate-r_binary64_1041`
136×	`unswap-sqr_binary64_1069`
118×	`unsub-neg_binary64_1095`
107×	`associate-*l/_binary64_1044`
76×	`associate-*r/_binary64_1043`
67×	`distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`
30×	`distribute-lft-neg-out_binary64_1060`
29×	`sub-neg_binary64_1094`
27×	`distribute-rgt-neg-out_binary64_1061`
24×	`div-sub_binary64_1106`
20×	`swap-sqr_binary64_1068`
19×	`sqr-pow_binary64_1073`
14×	`distribute-rgt-out_binary64_1054` `distribute-lft-out_binary64_1052`
12×	`mul0-rgt_binary64_1084` `mul0-lft_binary64_1083`
9×	`-rgt-identity_binary64_1091` `-lft-identity_binary64_1090`
6×	`cube-unmult_binary64_1138`
4×	`pow-plus_binary64_1164`
3×	`unpow1/2_binary64_1165` `+-commutative_binary64_1031`
2×	`div0_binary64_1082`
1×	`unpow2_binary64_1166` `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` `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-frac-neg_binary64_1064` `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-lft-out--_binary64_1053` `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 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	41
1	62	41
2	188	41
3	1060	41
4	3490	41
5	5205	41

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

27.7b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.2b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
10.4b	(sqrt.f64 (/.f64 d h))
11.0b	(sqrt.f64 (/.f64 d l))
13.3b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite437.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

12.6b

Rules

77×	`add-exp-log_binary64_1139`
41×	`prod-exp_binary64_1150`
32×	`add-sqr-sqrt_binary64_1123`
29×	`times-frac_binary64_1107`
26×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101` `sqrt-prod_binary64_1117`
21×	`add-cbrt-cube_binary64_1137`
16×	`div-exp_binary64_1152` `associate-r_binary64_1041`
14×	`sqrt-div_binary64_1118`
13×	`pow1_binary64_1162`
10×	`pow-exp_binary64_1169`
9×	`cbrt-unprod_binary64_1134` `frac-times_binary64_1111`
6×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`
4×	`pow-prod-down_binary64_1172` `add-log-exp_binary64_1140` `rem-sqrt-square_binary64_1114` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`div-inv_binary64_1098`
2×	`pow-to-exp_binary64_1170` `cbrt-undiv_binary64_1135` `associate-l_binary64_1042` `*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050`

Counts

4 → 127

Calls

4 calls:

21.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
3.0ms	(sqrt.f64 (/.f64 d h))
3.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 4714 to 2207 computations (53.2% saved)

series2.4s (7.2%)

Error

20.0b

Counts

4 → 50

Calls

4 calls:

1.4s	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
871.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
57.0ms	(sqrt.f64 (/.f64 d l))
53.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 2658 to 2317 computations (12.8% saved)

simplify164.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

383×	`associate-l_binary64_1042`
313×	`associate-r_binary64_1041`
302×	`distribute-rgt-in_binary64_1051`
278×	`distribute-lft-in_binary64_1050`
200×	`*-commutative_binary64_1032`
193×	`distribute-rgt-neg-in_binary64_1059`
175×	`distribute-lft-neg-in_binary64_1058`
138×	`cancel-sign-sub-inv_binary64_1067`
134×	`log-prod_binary64_1187`
130×	`exp-prod_binary64_1153`
126×	`associate-/l*_binary64_1046`
110×	`associate-*r/_binary64_1043`
88×	`times-frac_binary64_1107` `associate-*l/_binary64_1044`
75×	`unswap-sqr_binary64_1069`
74×	`distribute-neg-frac_binary64_1065`
68×	`associate-/r*_binary64_1045`
60×	`sqr-pow_binary64_1073`
53×	`cube-prod_binary64_1129`
49×	`log-div_binary64_1188`
48×	`distribute-lft-neg-out_binary64_1060`
44×	`swap-sqr_binary64_1068`
40×	`neg-sub0_binary64_1096`
39×	`*-lft-identity_binary64_1090`
38×	`unpow3_binary64_1167`
37×	`distribute-rgt-neg-out_binary64_1061`
36×	`sub-neg_binary64_1094` `*-rgt-identity_binary64_1091`
35×	`+-commutative_binary64_1031`
33×	`neg-mul-1_binary64_1097`
31×	`associate-/l/_binary64_1048`
28×	`associate-/r/_binary64_1047`
21×	`associate-+l+_binary64_1034`
18×	`distribute-rgt-out_binary64_1054`
15×	`cube-div_binary64_1130`
14×	`distribute-lft-out_binary64_1052`
11×	`log-pow_binary64_1190` `unpow1/2_binary64_1165`
10×	`rem-sqrt-square_binary64_1114`
9×	`cube-unmult_binary64_1138`
8×	`/-rgt-identity_binary64_1092` `associate-+r-_binary64_1035`
7×	`pow-plus_binary64_1164` `associate-+r+_binary64_1033`
6×	`unpow2_binary64_1166` `unpow1_binary64_1159` `mul-1-neg_binary64_1093`
5×	`cube-mult_binary64_1131` `unsub-neg_binary64_1095` `distribute-rgt1-in_binary64_1057`
4×	`exp-sqrt_binary64_1154` `pow-sqr_binary64_1074` `associate--l+_binary64_1038` `associate--r+_binary64_1037`
3×	`exp-sum_binary64_1147` `rem-square-sqrt_binary64_1113` `distribute-neg-in_binary64_1062`
2×	`div-sub_binary64_1106` `distribute-lft1-in_binary64_1056`
1×	`exp-diff_binary64_1149` `1-exp_binary64_1145` `exp-1-e_binary64_1144` `associate-+l-_binary64_1036`
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-neg_binary64_1148` `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` `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--r-_binary64_1040` `associate--l-_binary64_1039`

Counts

177 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	332	4611
1	760	4377
2	2817	4371
3	4773	4371
4	4979	4371

prune190.0ms (0.6%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	105	21	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	21	127

Error

10.6b

Counts

127 → 21

Compiler

Compiled 2987 to 1629 computations (45.5% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.9b	(/.f64 (.f64 M D) (.f64 d 2))
5.2b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.0b	(sqrt.f64 (/.f64 d l))
13.3b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite385.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

8.6b

Rules

93×	`add-exp-log_binary64_1139`
48×	`prod-exp_binary64_1150`
37×	`add-cbrt-cube_binary64_1137`
22×	`add-sqr-sqrt_binary64_1123`
20×	`div-exp_binary64_1152` `times-frac_binary64_1107`
19×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
16×	`pow1_binary64_1162` `cbrt-unprod_binary64_1134` `associate-r_binary64_1041`
13×	`sqrt-div_binary64_1118` `sqrt-prod_binary64_1117`
12×	`associate-*r/_binary64_1043`
10×	`pow-exp_binary64_1169`
9×	`frac-times_binary64_1111`
7×	`pow-prod-down_binary64_1172`
6×	`cbrt-undiv_binary64_1135` `associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`div-inv_binary64_1098`
2×	`pow-to-exp_binary64_1170` `associate-l_binary64_1042` `*-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045`

Counts

4 → 126

Calls

4 calls:

23.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 5947 to 2215 computations (62.8% saved)

series3.8s (11.7%)

Error

10.6b

Counts

4 → 51

Calls

4 calls:

2.7s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
878.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
199.0ms	(/.f64 (.f64 M D) (.f64 d 2))
64.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 4504 to 3652 computations (18.9% saved)

simplify238.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

655×	`associate-l_binary64_1042`
521×	`associate-r_binary64_1041`
298×	`*-commutative_binary64_1032`
213×	`log-prod_binary64_1187`
210×	`times-frac_binary64_1107`
176×	`associate-/l*_binary64_1046`
141×	`associate-*r/_binary64_1043`
122×	`log-div_binary64_1188`
117×	`associate-*l/_binary64_1044`
101×	`associate-/r*_binary64_1045`
96×	`cube-prod_binary64_1129`
95×	`exp-prod_binary64_1153` `sqr-pow_binary64_1073`
59×	`distribute-rgt-in_binary64_1051`
58×	`distribute-lft-in_binary64_1050`
51×	`sub-neg_binary64_1094`
49×	`neg-sub0_binary64_1096`
42×	`*-lft-identity_binary64_1090`
41×	`neg-mul-1_binary64_1097`
40×	`+-commutative_binary64_1031`
39×	`*-rgt-identity_binary64_1091`
36×	`cube-div_binary64_1130`
28×	`distribute-rgt-neg-in_binary64_1059`
27×	`associate-+l+_binary64_1034`
24×	`cancel-sign-sub-inv_binary64_1067`
23×	`swap-sqr_binary64_1068` `distribute-lft-neg-in_binary64_1058`
21×	`associate-/r/_binary64_1047`
20×	`associate-/l/_binary64_1048`
16×	`log-pow_binary64_1190`
13×	`cube-unmult_binary64_1138`
10×	`associate-+r+_binary64_1033`
9×	`mul-1-neg_binary64_1093` `/-rgt-identity_binary64_1092`
8×	`exp-sum_binary64_1147` `associate-+r-_binary64_1035`
7×	`rem-sqrt-square_binary64_1114` `div-sub_binary64_1106`
6×	`unpow3_binary64_1167` `pow-plus_binary64_1164` `unsub-neg_binary64_1095` `pow-sqr_binary64_1074` `unswap-sqr_binary64_1069` `distribute-neg-frac_binary64_1065` `distribute-lft-neg-out_binary64_1060`
5×	`unpow1/2_binary64_1165` `exp-sqrt_binary64_1154`
4×	`unpow1/3_binary64_1168` `unpow2_binary64_1166` `unpow1_binary64_1159` `exp-diff_binary64_1149` `cube-mult_binary64_1131` `associate--l+_binary64_1038` `associate--r+_binary64_1037`
3×	`distribute-rgt-neg-out_binary64_1061` `distribute-rgt-out_binary64_1054`
2×	`rem-square-sqrt_binary64_1113` `distribute-neg-in_binary64_1062` `distribute-rgt1-in_binary64_1057` `distribute-lft-out_binary64_1052` `associate-+l-_binary64_1036`
1×	`log-rec_binary64_1189` `exp-neg_binary64_1148` `1-exp_binary64_1145` `exp-1-e_binary64_1144` `sqr-abs_binary64_1116` `distribute-frac-neg_binary64_1064` `distribute-neg-out_binary64_1063` `associate--r-_binary64_1040` `associate--l-_binary64_1039`
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` `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-neg_binary64_1115` `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-lft1-in_binary64_1056` `distribute-rgt-out--_binary64_1055` `distribute-lft-out--_binary64_1053` `count-2_binary64_1049`

Counts

177 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	392	6191
1	982	5748
2	4141	5747
3	4849	5747
4	4997	5747
5	4947	5747

prune217.0ms (0.7%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	124	12	136
Fresh	7	13	20
Picked	1	0	1
Done	0	0	0
Total	132	25	157

Error

9.4b

Counts

157 → 25

Compiler

Compiled 3873 to 1824 computations (52.9% saved)

localize36.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 h)
3.9b	(/.f64 (.f64 M D) (.f64 d 2))
5.2b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
13.3b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite417.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

7.4b

Rules

102×	`add-exp-log_binary64_1139`
55×	`prod-exp_binary64_1150`
46×	`add-cbrt-cube_binary64_1137`
24×	`pow1_binary64_1162`
23×	`cbrt-unprod_binary64_1134`
20×	`div-exp_binary64_1152`
18×	`associate-*r/_binary64_1043`
16×	`associate-r_binary64_1041`
14×	`pow-prod-down_binary64_1172`
13×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
12×	`sqrt-div_binary64_1118`
10×	`pow-exp_binary64_1169` `times-frac_binary64_1107`
9×	`frac-times_binary64_1111`
6×	`cbrt-undiv_binary64_1135` `associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`cbrt-prod_binary64_1132`
2×	`pow-to-exp_binary64_1170` `associate-l_binary64_1042` `div-inv_binary64_1098` `*-commutative_binary64_1032` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `pow1/3_binary64_1183`

Counts

4 → 118

Calls

4 calls:

31.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
1.0ms	(cbrt.f64 h)

Compiler

Compiled 6839 to 2143 computations (68.7% saved)

series4.7s (14.4%)

Error

7.9b

Counts

4 → 51

Calls

4 calls:

3.5s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
859.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
209.0ms	(/.f64 (.f64 M D) (.f64 d 2))
110.0ms	(cbrt.f64 h)

Compiler

Compiled 5721 to 4254 computations (25.6% saved)

simplify224.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

431×	`*-commutative_binary64_1032`
211×	`times-frac_binary64_1107`
184×	`associate-/l*_binary64_1046`
163×	`log-prod_binary64_1187`
160×	`distribute-rgt-neg-in_binary64_1059`
147×	`associate-*r/_binary64_1043`
138×	`log-div_binary64_1188`
117×	`unswap-sqr_binary64_1069`
116×	`associate-/r_binary64_1045` `associate-l/_binary64_1044`
115×	`sqr-pow_binary64_1073`
113×	`distribute-neg-frac_binary64_1065`
98×	`cancel-sign-sub-inv_binary64_1067`
88×	`associate-r_binary64_1041`
87×	`associate-l_binary64_1042`
83×	`exp-prod_binary64_1153` `swap-sqr_binary64_1068`
70×	`sub-neg_binary64_1094`
67×	`distribute-rgt-in_binary64_1051`
66×	`distribute-lft-in_binary64_1050`
65×	`cube-prod_binary64_1129`
56×	`neg-sub0_binary64_1096`
54×	`neg-mul-1_binary64_1097`
47×	`distribute-lft-neg-out_binary64_1060` `+-commutative_binary64_1031`
42×	`distribute-rgt-neg-out_binary64_1061`
41×	`cube-div_binary64_1130`
37×	`associate-+l+_binary64_1034`
29×	`distribute-lft-neg-in_binary64_1058`
28×	`*-rgt-identity_binary64_1091`
25×	`div-sub_binary64_1106`
22×	`*-lft-identity_binary64_1090`
20×	`cube-unmult_binary64_1138`
19×	`exp-diff_binary64_1149` `associate-/r/_binary64_1047`
18×	`exp-sum_binary64_1147`
16×	`log-pow_binary64_1190` `unsub-neg_binary64_1095` `associate-+r+_binary64_1033`
15×	`associate-/l/_binary64_1048` `associate-+r-_binary64_1035`
12×	`pow-sqr_binary64_1074`
10×	`distribute-neg-out_binary64_1063`
9×	`unpow1/3_binary64_1168`
8×	`rem-sqrt-square_binary64_1114`
7×	`associate-+l-_binary64_1036`
6×	`exp-neg_binary64_1148` `/-rgt-identity_binary64_1092` `distribute-frac-neg_binary64_1064`
5×	`unpow3_binary64_1167` `unpow1/2_binary64_1165` `exp-sqrt_binary64_1154`
4×	`log-rec_binary64_1189` `unpow2_binary64_1166` `pow-plus_binary64_1164` `exp-to-pow_binary64_1163` `unpow1_binary64_1159` `distribute-neg-in_binary64_1062` `associate--l+_binary64_1038` `associate--r+_binary64_1037`
3×	`cube-mult_binary64_1131` `distribute-rgt-out_binary64_1054`
2×	`sqr-abs_binary64_1116` `rem-square-sqrt_binary64_1113` `mul-1-neg_binary64_1093` `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-lft_binary64_1126`
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` `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` `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-cbrt-cube_binary64_1125` `rem-cube-cbrt_binary64_1124` `sqr-neg_binary64_1115` `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-lft1-in_binary64_1056` `distribute-rgt-out--_binary64_1055` `distribute-lft-out--_binary64_1053` `count-2_binary64_1049` `associate--r-_binary64_1040`

Counts

169 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	426	7854
1	1122	7098
2	3172	7097
3	4858	7097
4	4966	7097

prune238.0ms (0.7%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	134	7	141
Fresh	2	22	24
Picked	1	0	1
Done	0	0	0
Total	137	29	166

Error

7.9b

Counts

166 → 29

Compiler

Compiled 4771 to 2027 computations (57.5% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.9b	(/.f64 (.f64 M D) (.f64 2 d))
5.2b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))
5.8b	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
7.2b	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)

rewrite473.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

7.0b

Rules

104×	`add-exp-log_binary64_1139`
55×	`prod-exp_binary64_1150`
48×	`add-cbrt-cube_binary64_1137`
24×	`pow1_binary64_1162`
23×	`cbrt-unprod_binary64_1134`
21×	`div-exp_binary64_1152`
17×	`associate-*r/_binary64_1043`
15×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
14×	`pow-prod-down_binary64_1172` `cancel-sign-sub-inv_binary64_1067`
12×	`add-cube-cbrt_binary64_1136` `sqrt-div_binary64_1118`
10×	`pow-exp_binary64_1169` `times-frac_binary64_1107`
9×	`frac-times_binary64_1111`
8×	`distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`
7×	`cbrt-undiv_binary64_1135` `associate-r_binary64_1041`
6×	`associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098` `associate-/r_binary64_1045` `associate-l*_binary64_1042` `flip3--_binary64_1105` `flip--_binary64_1076`
2×	`pow-to-exp_binary64_1170` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `-commutative_binary64_1032` `sub-neg_binary64_1094` `difference-of-squares_binary64_1070`
1×	`distribute-lft-out--_binary64_1053`

Counts

4 → 130

Calls

4 calls:

36.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))
11.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
8.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 7829 to 2531 computations (67.7% saved)

series5.2s (15.7%)

Error

7.9b

Counts

4 → 60

Calls

4 calls:

3.5s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))
849.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
596.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
197.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 6513 to 4790 computations (26.5% saved)

simplify269.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

451×	`*-commutative_binary64_1032`
227×	`times-frac_binary64_1107`
213×	`associate-/l*_binary64_1046`
160×	`log-prod_binary64_1187`
148×	`log-div_binary64_1188`
147×	`associate-*r/_binary64_1043`
138×	`associate-*l/_binary64_1044`
135×	`distribute-neg-frac_binary64_1065`
128×	`associate-/r*_binary64_1045`
104×	`sqr-pow_binary64_1073`
102×	`associate-r_binary64_1041`
94×	`unpow3_binary64_1167`
88×	`distribute-rgt-neg-out_binary64_1061`
87×	`sub-neg_binary64_1094` `swap-sqr_binary64_1068`
83×	`associate-l_binary64_1042`
82×	`neg-mul-1_binary64_1097` `neg-sub0_binary64_1096` `cancel-sign-sub-inv_binary64_1067`
71×	`distribute-rgt-in_binary64_1051`
70×	`distribute-lft-in_binary64_1050`
67×	`exp-prod_binary64_1153`
66×	`cube-prod_binary64_1129`
55×	`cube-div_binary64_1130` `unswap-sqr_binary64_1069`
48×	`+-commutative_binary64_1031`
45×	`associate-/r/_binary64_1047`
36×	`div-sub_binary64_1106`
33×	`*-rgt-identity_binary64_1091`
31×	`distribute-lft-neg-out_binary64_1060`
30×	`distribute-rgt-neg-in_binary64_1059`
25×	`associate-+l+_binary64_1034`
23×	`*-lft-identity_binary64_1090`
22×	`unsub-neg_binary64_1095` `distribute-lft-neg-in_binary64_1058` `associate-/l/_binary64_1048`
20×	`associate-+r+_binary64_1033`
18×	`exp-sum_binary64_1147`
17×	`exp-diff_binary64_1149` `cube-unmult_binary64_1138`
15×	`associate--l+_binary64_1038`
14×	`distribute-frac-neg_binary64_1064`
12×	`log-pow_binary64_1190`
10×	`distribute-neg-out_binary64_1063`
9×	`pow-sqr_binary64_1074`
7×	`unpow1/3_binary64_1168` `associate-+r-_binary64_1035`
6×	`exp-neg_binary64_1148` `associate-+l-_binary64_1036`
5×	`log-rec_binary64_1189` `rem-sqrt-square_binary64_1114`
4×	`unpow2_binary64_1166` `unpow1/2_binary64_1165` `pow-plus_binary64_1164` `exp-to-pow_binary64_1163` `unpow1_binary64_1159` `cube-mult_binary64_1131` `/-rgt-identity_binary64_1092` `associate--r+_binary64_1037`
3×	`exp-sqrt_binary64_1154` `rem-square-sqrt_binary64_1113` `div0_binary64_1082`
2×	`sqr-abs_binary64_1116` `distribute-neg-in_binary64_1062` `distribute-rgt1-in_binary64_1057` `associate--l-_binary64_1039`
1×	`1-exp_binary64_1145` `exp-1-e_binary64_1144` `rem-3cbrt-lft_binary64_1126` `mul-1-neg_binary64_1093` `distribute-rgt-out_binary64_1054`
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` `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` `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-cbrt-cube_binary64_1125` `rem-cube-cbrt_binary64_1124` `sqr-neg_binary64_1115` `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` `*-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-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_1040`

Counts

190 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	437	9932
1	1182	9027
2	3395	9026
3	4741	9026
4	4963	9026

prune137.0ms (0.4%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	2	26	28
Picked	1	0	1
Done	0	0	0
Total	139	28	167

Error

7.2b

Counts

167 → 28

Compiler

Compiled 2627 to 916 computations (65.1% saved)

regimes6.3s (19%)

Accuracy

Total 3.8b remaining (28.3%)

Threshold costs 0b (0%)

Compiler

Compiled 78985 to 56866 computations (28% saved)

bsearch23.0ms (0.1%)

Compiler: Compiled 35 to 31 computations (11.4% saved)

simplify26.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

40×	`*-commutative_binary64_1032`
22×	`sub-neg_binary64_1094` `+-commutative_binary64_1031`
21×	`neg-mul-1_binary64_1097` `neg-sub0_binary64_1096`
18×	`distribute-rgt-neg-in_binary64_1059`
16×	`distribute-lft-neg-in_binary64_1058`
4×	`cancel-sign-sub-inv_binary64_1067` `distribute-lft-neg-out_binary64_1060`
3×	`distribute-neg-frac_binary64_1065` `distribute-rgt-neg-out_binary64_1061`
2×	`unsub-neg_binary64_1095`
1×	`1-exp_binary64_1145` `*-lft-identity_binary64_1090`
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` `mul-1-neg_binary64_1093` `/-rgt-identity_binary64_1092` `*-rgt-identity_binary64_1091` `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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	360
1	91	360
2	109	360
3	131	360
4	156	360
5	172	360
6	183	360
7	195	360
8	214	360
9	227	360
10	237	360
11	241	360
12	237	360

end32.0ms (0.1%)

Remove: (sort M D)
Compiler: Compiled 675 to 282 computations (58.2% saved)

sample4.7s (14.4%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
1.0s	8301×	body	128	nan
642.0ms	4749×	body	128	invalid

Compiler

Compiled 1409 to 933 computations (33.8% saved)

Iter	Nodes	Cost
0	66	360
1	91	360
2	109	360
3	131	360
4	156	360
5	172	360
6	183	360
7	195	360
8	214	360
9	227	360
10	237	360
11	241	360
12	237	360

Iter	Nodes	Cost
0	66	360
1	91	360
2	109	360
3	131	360
4	156	360
5	172	360
6	183	360
7	195	360
8	214	360
9	227	360
10	237	360
11	241	360
12	237	360

Details

analyze2.0s (6.1%)

sample150.0ms (0.5%)

simplify39.0ms (0.1%)

prune5.0ms (0%)

localize20.0ms (0.1%)

rewrite437.0ms (1.3%)

series2.4s (7.2%)

simplify164.0ms (0.5%)

prune190.0ms (0.6%)

localize27.0ms (0.1%)

rewrite385.0ms (1.2%)

series3.8s (11.7%)

simplify238.0ms (0.7%)

prune217.0ms (0.7%)

localize36.0ms (0.1%)

rewrite417.0ms (1.3%)

series4.7s (14.4%)

simplify224.0ms (0.7%)

prune238.0ms (0.7%)

localize32.0ms (0.1%)

rewrite473.0ms (1.4%)

series5.2s (15.7%)

simplify269.0ms (0.8%)

prune137.0ms (0.4%)

regimes6.3s (19%)

bsearch23.0ms (0.1%)

simplify26.0ms (0.1%)

end32.0ms (0.1%)

sample4.7s (14.4%)

Profiling

Iter	Nodes	Cost
0	66	360
1	91	360
2	109	360
3	131	360
4	156	360
5	172	360
6	183	360
7	195	360
8	214	360
9	227	360
10	237	360
11	241	360
12	237	360