Details

analyze1.9s (42.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

Compiler

Compiled 25 to 23 computations (8% saved)

sample86.0ms (1.9%)

Algorithm

1×

intervals

Results

39.0ms	73×	body	1024	valid
14.0ms	30×	body	512	valid
14.0ms	133×	body	128	valid
5.0ms	20×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify183.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

763×	`sqr-pow_binary64_1073`
636×	`associate-/l/_binary64_1048`
617×	`pow-sqr_binary64_1074`
329×	`associate-/l*_binary64_1046`
309×	`*-commutative_binary64_1032`
300×	`unswap-sqr_binary64_1069`
288×	`times-frac_binary64_1107`
243×	`associate-*l/_binary64_1044`
212×	`associate-/r*_binary64_1045`
189×	`associate-l_binary64_1042`
154×	`associate-/r/_binary64_1047`
148×	`pow-plus_binary64_1164`
140×	`associate-*r/_binary64_1043`
138×	`associate-r_binary64_1041`
111×	`cube-prod_binary64_1129`
54×	`unpow3_binary64_1167`
49×	`cube-mult_binary64_1131`
28×	`+-commutative_binary64_1031`
21×	`associate-+l+_binary64_1034`
18×	`distribute-rgt-in_binary64_1051`
16×	`distribute-lft-in_binary64_1050`
12×	`swap-sqr_binary64_1068`
7×	`cube-unmult_binary64_1138`
2×	`associate-+r+_binary64_1033`
1×	`unpow2_binary64_1166` `unpow1_binary64_1159` `1-exp_binary64_1145` `-rgt-identity_binary64_1091` `-inverses_binary64_1081` `rgt-mult-inverse_binary64_1078` `distribute-rgt1-in_binary64_1057` `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` `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` `unpow1/2_binary64_1165` `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-div_binary64_1130` `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-sqrt-square_binary64_1114` `rem-square-sqrt_binary64_1113` `div-sub_binary64_1106` `neg-mul-1_binary64_1097` `neg-sub0_binary64_1096` `unsub-neg_binary64_1095` `sub-neg_binary64_1094` `mul-1-neg_binary64_1093` `/-rgt-identity_binary64_1092` `*-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` `mul0-rgt_binary64_1084` `mul0-lft_binary64_1083` `div0_binary64_1082` `+-inverses_binary64_1080` `lft-mult-inverse_binary64_1079` `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-inv_binary64_1067` `cancel-sign-sub_binary64_1066` `distribute-neg-frac_binary64_1065` `distribute-frac-neg_binary64_1064` `distribute-neg-out_binary64_1063` `distribute-neg-in_binary64_1062` `distribute-rgt-neg-out_binary64_1061` `distribute-lft-neg-out_binary64_1060` `distribute-rgt-neg-in_binary64_1059` `distribute-lft-neg-in_binary64_1058` `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` `associate--r-_binary64_1040` `associate--l-_binary64_1039` `associate--l+_binary64_1038` `associate--r+_binary64_1037` `associate-+l-_binary64_1036` `associate-+r-_binary64_1035`

Counts

1 → 5

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	37	37
2	82	37
3	196	37
4	649	37
5	1920	37
6	2072	37
7	2619	37
8	2792	37
9	3234	37
10	4159	37

prune8.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	5	0	5
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	5	1	6

Error

21.7b

Counts

6 → 1

Compiler

Compiled 144 to 120 computations (16.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
7.9b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
12.5b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite226.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

21.6b

Rules

28×	`add-exp-log_binary64_1139`
20×	`pow1_binary64_1162`
18×	`add-cbrt-cube_binary64_1137`
15×	`*-un-lft-identity_binary64_1101`
12×	`add-sqr-sqrt_binary64_1123` `prod-exp_binary64_1150`
11×	`add-cube-cbrt_binary64_1136`
10×	`associate-r_binary64_1041`
9×	`pow-prod-down_binary64_1172` `cbrt-unprod_binary64_1134`
8×	`sqrt-prod_binary64_1117`
7×	`unpow-prod-down_binary64_1180`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `pow-exp_binary64_1169`
3×	`times-frac_binary64_1107` `pow-unpow_binary64_1178` `div-exp_binary64_1152`
2×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `distribute-lft-out_binary64_1052` `associate-r/_binary64_1043` `associate-l_binary64_1042` `-commutative_binary64_1032`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `div-inv_binary64_1098` `pow-pow_binary64_1173` `pow-to-exp_binary64_1170` `unpow2_binary64_1166` `sqr-pow_binary64_1073`

Counts

4 → 86

Calls

4 calls:

15.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
5.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3141 to 2524 computations (19.6% saved)

series1.8s (40.3%)

Error

0.1b

Counts

4 → 58

Calls

4 calls:

757.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
514.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
341.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
125.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4276 to 3662 computations (14.4% saved)

simplify246.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

817×	`times-frac_binary64_1107`
301×	`associate-l_binary64_1042`
228×	`associate-r_binary64_1041`
168×	`cancel-sign-sub-inv_binary64_1067`
160×	`*-commutative_binary64_1032`
146×	`distribute-rgt-in_binary64_1051`
131×	`distribute-rgt-neg-in_binary64_1059`
123×	`sqr-pow_binary64_1073`
117×	`unswap-sqr_binary64_1069`
112×	`distribute-lft-neg-in_binary64_1058`
72×	`sub-neg_binary64_1094`
69×	`distribute-neg-frac_binary64_1065`
56×	`log-prod_binary64_1187`
54×	`associate-/r*_binary64_1045`
51×	`neg-sub0_binary64_1096` `associate-/l*_binary64_1046`
50×	`neg-mul-1_binary64_1097`
49×	`exp-prod_binary64_1153`
47×	`+-commutative_binary64_1031`
46×	`associate-*r/_binary64_1043`
40×	`associate-*l/_binary64_1044`
39×	`cube-prod_binary64_1129`
37×	`swap-sqr_binary64_1068`
30×	`pow-sqr_binary64_1074`
29×	`*-lft-identity_binary64_1090`
24×	`pow-plus_binary64_1164`
21×	`*-rgt-identity_binary64_1091`
20×	`distribute-neg-in_binary64_1062`
19×	`distribute-lft-neg-out_binary64_1060` `associate--r+_binary64_1037`
16×	`unpow2_binary64_1166` `associate-+l+_binary64_1034`
15×	`unpow1_binary64_1159` `unsub-neg_binary64_1095`
14×	`distribute-rgt-out_binary64_1054` `distribute-lft-out--_binary64_1053`
12×	`distribute-rgt-out--_binary64_1055` `distribute-lft-in_binary64_1050`
11×	`log-div_binary64_1188`
10×	`cube-unmult_binary64_1138`
9×	`associate--l+_binary64_1038` `associate-+r+_binary64_1033`
8×	`log-pow_binary64_1190` `cube-div_binary64_1130` `associate-/r/_binary64_1047`
6×	`unpow3_binary64_1167` `pow-base-1_binary64_1161` `rem-sqrt-square_binary64_1114`
5×	`difference-of-squares_binary64_1070` `distribute-rgt1-in_binary64_1057` `distribute-lft-out_binary64_1052`
4×	`cube-mult_binary64_1131`
3×	`difference-of-sqr-1_binary64_1071` `associate-+r-_binary64_1035`
2×	`rem-square-sqrt_binary64_1113` `+-rgt-identity_binary64_1086` `distribute-rgt-neg-out_binary64_1061`
1×	`1-exp_binary64_1145` `exp-1-e_binary64_1144` `rem-3cbrt-rft_binary64_1127` `rem-3cbrt-lft_binary64_1126` `mul-1-neg_binary64_1093` `*-inverses_binary64_1081` `rgt-mult-inverse_binary64_1078` `distribute-lft1-in_binary64_1056` `associate-/l/_binary64_1048` `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` `unpow1/2_binary64_1165` `exp-to-pow_binary64_1163` `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-0_binary64_1143` `rem-log-exp_binary64_1142` `rem-exp-log_binary64_1141` `cube-neg_binary64_1128` `rem-cbrt-cube_binary64_1125` `rem-cube-cbrt_binary64_1124` `sqr-abs_binary64_1116` `sqr-neg_binary64_1115` `div-sub_binary64_1106` `/-rgt-identity_binary64_1092` `remove-double-neg_binary64_1089` `sub0-neg_binary64_1088` `--rgt-identity_binary64_1087` `+-lft-identity_binary64_1085` `mul0-rgt_binary64_1084` `mul0-lft_binary64_1083` `div0_binary64_1082` `+-inverses_binary64_1080` `lft-mult-inverse_binary64_1079` `remove-double-div_binary64_1077` `difference-of-sqr--1_binary64_1072` `cancel-sign-sub_binary64_1066` `distribute-frac-neg_binary64_1064` `distribute-neg-out_binary64_1063` `count-2_binary64_1049` `associate--r-_binary64_1040` `associate--l-_binary64_1039`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	252	4122
1	639	3786
2	2218	3745

Details

analyze1.9s (42.8%)

sample86.0ms (1.9%)

simplify183.0ms (4.1%)

prune8.0ms (0.2%)

localize14.0ms (0.3%)

rewrite226.0ms (5%)

series1.8s (40.3%)

simplify246.0ms (5.4%)

end0.0ms (0%)

Profiling