Details

analyze2.9s (10.4%)

Algorithm

1×	search
2×	egg-herbie

Rules

668×	`times-frac_binary64_1107`
359×	`cancel-sign-sub-inv_binary64_1067`
300×	`associate-/l*_binary64_1046`
286×	`*-commutative_binary64_1032`
260×	`neg-mul-1_binary64_1097` `neg-sub0_binary64_1096`
226×	`distribute-rgt-neg-in_binary64_1059`
200×	`distribute-neg-frac_binary64_1065`
197×	`distribute-lft-neg-in_binary64_1058`
155×	`associate-/r/_binary64_1047`
122×	`associate-/l/_binary64_1048`
109×	`sub-neg_binary64_1094`
93×	`associate-/r*_binary64_1045`
85×	`swap-sqr_binary64_1068`
81×	`associate-*r/_binary64_1043`
65×	`associate-*l/_binary64_1044`
49×	`sqr-pow_binary64_1073`
42×	`associate-l_binary64_1042`
30×	`div-sub_binary64_1106`
29×	`distribute-lft-neg-out_binary64_1060`
28×	`associate-r_binary64_1041`
15×	`sub0-neg_binary64_1088` `associate-+l-_binary64_1036` `+-commutative_binary64_1031`
13×	`unpow2_binary64_1166`
12×	`unpow1/2_binary64_1165` `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` `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` `--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` `unswap-sqr_binary64_1069` `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-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` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050` `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	125	432
1	374	432
2	1139	432
3	2964	432
4	5015	432
0	6	6
1	6	6

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

Symmetry

(sort M D)

Compiler

Compiled 19 to 19 computations (0% saved)

sample65.0ms (0.2%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
7.0ms	95×	body	128	nan
2.0ms	30×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify44.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

893×	`div-sub_binary64_1106`
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`
263×	`associate-/l/_binary64_1048`
254×	`*-commutative_binary64_1032`
227×	`times-frac_binary64_1107`
189×	`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`
78×	`associate-*r/_binary64_1043`
77×	`associate-l_binary64_1042`
69×	`associate-r_binary64_1041`
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×	`pow-plus_binary64_1164` `cube-unmult_binary64_1138` `+-commutative_binary64_1031`
2×	`mul0-rgt_binary64_1084` `mul0-lft_binary64_1083` `div0_binary64_1082` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`
1×	`unpow3_binary64_1167` `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` `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 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	42	27
2	111	27
3	718	27
4	2816	27
5	4686	27
6	6100	27

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

13.8b

Counts

1 → 1

Compiler

Compiled 18 to 18 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.2b	(/.f64 (.f64 M D) (.f64 2 d))
12.2b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite309.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

7.3b

Rules

67×	`add-exp-log_binary64_1139`
38×	`add-sqr-sqrt_binary64_1123`
27×	`prod-exp_binary64_1150`
23×	`add-cbrt-cube_binary64_1137`
19×	`div-exp_binary64_1152` `associate-r_binary64_1041`
17×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
15×	`times-frac_binary64_1107`
13×	`associate-l_binary64_1042`
10×	`pow-exp_binary64_1169` `unswap-sqr_binary64_1069`
7×	`pow1_binary64_1162` `cbrt-unprod_binary64_1134` `unpow-prod-down_binary64_1180` `sqrt-prod_binary64_1117`
5×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
3×	`unpow2_binary64_1166` `sqr-pow_binary64_1073` `associate-*r/_binary64_1043` `div-inv_binary64_1098`
2×	`pow-to-exp_binary64_1170` `*-commutative_binary64_1032` `flip3--_binary64_1105` `flip--_binary64_1076`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `pow-prod-down_binary64_1172`

Counts

4 → 116

Calls

4 calls:

12.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

Compiler

Compiled 3226 to 1835 computations (43.1% saved)

series2.2s (8%)

Error

6.7b

Counts

4 → 67

Calls

4 calls:

806.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
747.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
456.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
183.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3162 to 2984 computations (5.6% saved)

simplify160.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

286×	`associate-l_binary64_1042`
282×	`distribute-rgt-neg-in_binary64_1059`
271×	`times-frac_binary64_1107`
263×	`distribute-lft-neg-in_binary64_1058`
256×	`associate-r_binary64_1041`
223×	`associate-/l*_binary64_1046`
199×	`log-prod_binary64_1187`
179×	`distribute-neg-frac_binary64_1065`
164×	`associate-*r/_binary64_1043`
157×	`cancel-sign-sub-inv_binary64_1067`
155×	`*-commutative_binary64_1032`
137×	`associate-/r*_binary64_1045`
134×	`log-div_binary64_1188`
132×	`associate-*l/_binary64_1044`
94×	`unpow3_binary64_1167`
83×	`unswap-sqr_binary64_1069`
73×	`cube-prod_binary64_1129`
66×	`swap-sqr_binary64_1068`
60×	`neg-sub0_binary64_1096`
59×	`exp-prod_binary64_1153`
58×	`sqr-pow_binary64_1073`
55×	`neg-mul-1_binary64_1097`
50×	`sub-neg_binary64_1094`
39×	`cube-div_binary64_1130`
37×	`-rgt-identity_binary64_1091` `-lft-identity_binary64_1090`
30×	`+-commutative_binary64_1031`
23×	`associate-/r/_binary64_1047`
22×	`log-pow_binary64_1190`
19×	`associate-/l/_binary64_1048`
12×	`distribute-lft-neg-out_binary64_1060`
10×	`distribute-rgt-out_binary64_1054`
8×	`unpow2_binary64_1166` `unpow1/2_binary64_1165` `pow-plus_binary64_1164` `unpow1_binary64_1159` `cube-unmult_binary64_1138` `/-rgt-identity_binary64_1092`
7×	`distribute-rgt1-in_binary64_1057`
6×	`associate-+r-_binary64_1035`
5×	`mul-1-neg_binary64_1093` `pow-sqr_binary64_1074` `distribute-lft-out_binary64_1052` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`
4×	`exp-sqrt_binary64_1154` `rem-sqrt-square_binary64_1114` `distribute-rgt-neg-out_binary64_1061` `associate--l+_binary64_1038` `associate--r+_binary64_1037` `associate-+l+_binary64_1034`
3×	`cube-mult_binary64_1131` `unsub-neg_binary64_1095`
2×	`rem-square-sqrt_binary64_1113` `distribute-neg-in_binary64_1062` `distribute-lft1-in_binary64_1056` `associate-+r+_binary64_1033`
1×	`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-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` `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

183 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	4240
1	693	3985
2	3021	3984
3	4652	3984
4	4998	3984

prune198.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	128	11	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	11	140

Error

4.5b

Counts

140 → 11

Compiler

Compiled 2293 to 1348 computations (41.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.9b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
4.0b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
4.2b	(/.f64 (.f64 M D) (.f64 2 d))
6.4b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)

rewrite288.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

Rules

67×	`add-exp-log_binary64_1139`
26×	`prod-exp_binary64_1150`
23×	`add-cbrt-cube_binary64_1137`
20×	`div-exp_binary64_1152` `add-sqr-sqrt_binary64_1123`
13×	`*-un-lft-identity_binary64_1101`
10×	`pow-exp_binary64_1169` `add-cube-cbrt_binary64_1136` `associate-r_binary64_1041`
6×	`cbrt-undiv_binary64_1135` `cbrt-unprod_binary64_1134` `sqrt-prod_binary64_1117` `unpow-prod-down_binary64_1180`
5×	`pow1_binary64_1162` `times-frac_binary64_1107`
4×	`add-log-exp_binary64_1140` `associate-/r*_binary64_1045` `unswap-sqr_binary64_1069`
3×	`div-inv_binary64_1098` `associate-l_binary64_1042`
2×	`pow-to-exp_binary64_1170` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l*_binary64_1046` `sqrt-div_binary64_1118` `difference-of-squares_binary64_1070` `unpow2_binary64_1166` `sqr-pow_binary64_1073`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `distribute-lft-out--_binary64_1053` `rem-sqrt-square_binary64_1114` `*-commutative_binary64_1032`

Counts

4 → 99

Calls

4 calls:

8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
8.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2610 to 1612 computations (38.2% saved)

series2.0s (7.2%)

Error

4.5b

Counts

4 → 58

Calls

4 calls:

815.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
533.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
438.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
189.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2650 to 2558 computations (3.5% saved)

simplify100.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

819×	`associate-/r/_binary64_1047`
263×	`times-frac_binary64_1107`
225×	`distribute-rgt-neg-in_binary64_1059`
216×	`associate-/l*_binary64_1046`
213×	`distribute-lft-neg-in_binary64_1058`
174×	`distribute-neg-frac_binary64_1065`
154×	`associate-l_binary64_1042`
148×	`associate-r_binary64_1041`
130×	`associate-/r*_binary64_1045`
107×	`cancel-sign-sub-inv_binary64_1067`
97×	`associate-*r/_binary64_1043`
96×	`associate-*l/_binary64_1044`
89×	`*-commutative_binary64_1032`
75×	`unswap-sqr_binary64_1069`
71×	`log-prod_binary64_1187`
63×	`swap-sqr_binary64_1068`
62×	`log-div_binary64_1188`
57×	`sub-neg_binary64_1094`
52×	`exp-prod_binary64_1153`
51×	`cube-prod_binary64_1129`
50×	`sqr-pow_binary64_1073`
49×	`neg-sub0_binary64_1096`
48×	`cube-div_binary64_1130`
46×	`neg-mul-1_binary64_1097`
30×	`distribute-rgt-in_binary64_1051`
26×	`associate-/l/_binary64_1048`
24×	`distribute-lft-in_binary64_1050`
23×	`+-commutative_binary64_1031`
20×	`*-rgt-identity_binary64_1091`
19×	`*-lft-identity_binary64_1090`
12×	`/-rgt-identity_binary64_1092`
11×	`associate--l+_binary64_1038`
10×	`log-pow_binary64_1190`
8×	`unpow2_binary64_1166` `unpow1/2_binary64_1165` `pow-plus_binary64_1164` `unpow1_binary64_1159`
7×	`cube-unmult_binary64_1138` `distribute-lft-neg-out_binary64_1060`
5×	`unpow3_binary64_1167` `distribute-rgt1-in_binary64_1057`
4×	`log-rec_binary64_1189` `exp-sqrt_binary64_1154` `rem-sqrt-square_binary64_1114` `unsub-neg_binary64_1095` `pow-sqr_binary64_1074` `associate--r+_binary64_1037` `associate-+l+_binary64_1034`
3×	`cube-mult_binary64_1131` `div-sub_binary64_1106` `mul-1-neg_binary64_1093` `distribute-lft-out_binary64_1052`
2×	`rem-square-sqrt_binary64_1113` `distribute-neg-in_binary64_1062` `distribute-rgt-neg-out_binary64_1061` `distribute-rgt-out_binary64_1054` `associate-+r+_binary64_1033`
1×	`1-exp_binary64_1145` `exp-1-e_binary64_1144` `rem-3cbrt-rft_binary64_1127` `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` `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-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-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_1036` `associate-+r-_binary64_1035`

Counts

157 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	3228
1	530	3042
2	2326	3033
3	5149	3033

prune118.0ms (0.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	97	5	102
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	101	12	113

Error

3.8b

Counts

113 → 12

Compiler

Compiled 1183 to 785 computations (33.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.9b	(*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2))
4.0b	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)))
5.6b	(/.f64 M (/.f64 2 (/.f64 D d)))
6.4b	(/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)

rewrite1.5s (5.3%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

735×	`times-frac_binary64_1107`
366×	`add-sqr-sqrt_binary64_1123`
347×	`*-un-lft-identity_binary64_1101`
344×	`add-cube-cbrt_binary64_1136`
142×	`associate-r_binary64_1041`
141×	`unpow-prod-down_binary64_1180`
55×	`add-exp-log_binary64_1139`
47×	`associate-/r*_binary64_1045`
31×	`div-inv_binary64_1098`
25×	`div-exp_binary64_1152`
20×	`add-cbrt-cube_binary64_1137`
12×	`prod-exp_binary64_1150`
9×	`associate-/r/_binary64_1047`
8×	`pow-exp_binary64_1169` `cbrt-undiv_binary64_1135`
7×	`unswap-sqr_binary64_1069`
6×	`sqrt-prod_binary64_1117`
5×	`pow1_binary64_1162`
4×	`add-log-exp_binary64_1140` `associate-/l*_binary64_1046`
3×	`associate-l_binary64_1042`
2×	`pow-to-exp_binary64_1170` `cbrt-unprod_binary64_1134` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `sqrt-div_binary64_1118` `difference-of-squares_binary64_1070` `unpow2_binary64_1166` `sqr-pow_binary64_1073`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `distribute-lft-out--_binary64_1053` `rem-sqrt-square_binary64_1114` `*-commutative_binary64_1032`

Counts

4 → 407

Calls

4 calls:

63.0ms	(*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2))
34.0ms	(/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)
14.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)))

Compiler

Compiled 13034 to 7522 computations (42.3% saved)

series2.0s (7.2%)

Error

3.8b

Counts

4 → 58

Calls

4 calls:

832.0ms	(/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)
526.0ms	(*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2))
440.0ms	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)))
167.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))

Compiler

Compiled 2650 to 2558 computations (3.5% saved)

simplify230.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

723×	`associate-*l/_binary64_1044`
550×	`associate-/r/_binary64_1047`
394×	`associate-/l/_binary64_1048`
288×	`associate-/r*_binary64_1045`
266×	`associate-/l*_binary64_1046`
254×	`sqr-pow_binary64_1073`
171×	`times-frac_binary64_1107`
162×	`*-commutative_binary64_1032`
125×	`unpow2_binary64_1166`
124×	`unpow1_binary64_1159`
115×	`swap-sqr_binary64_1068`
27×	`sub-neg_binary64_1094`
26×	`distribute-rgt-neg-in_binary64_1059`
25×	`distribute-neg-frac_binary64_1065`
23×	`neg-sub0_binary64_1096`
21×	`neg-mul-1_binary64_1097` `distribute-lft-neg-in_binary64_1058`
18×	`associate-*r/_binary64_1043`
13×	`log-div_binary64_1188` `remove-double-div_binary64_1077` `associate-l_binary64_1042`
12×	`cancel-sign-sub-inv_binary64_1067`
11×	`/-rgt-identity_binary64_1092`
10×	`log-prod_binary64_1187`
9×	`associate-r_binary64_1041` `+-commutative_binary64_1031`
8×	`exp-prod_binary64_1153` `unswap-sqr_binary64_1069`
6×	`cube-div_binary64_1130`
5×	`cube-unmult_binary64_1138` `rem-square-sqrt_binary64_1113` `associate--l+_binary64_1038`
4×	`pow-plus_binary64_1164` `rem-sqrt-square_binary64_1114`
3×	`unpow3_binary64_1167` `cube-prod_binary64_1129` `mul-1-neg_binary64_1093` `distribute-neg-in_binary64_1062` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`
2×	`log-pow_binary64_1190` `*-lft-identity_binary64_1090` `distribute-rgt1-in_binary64_1057` `associate--r-_binary64_1040`
1×	`log-rec_binary64_1189` `unpow1/2_binary64_1165` `1-exp_binary64_1145` `cube-mult_binary64_1131` `*-rgt-identity_binary64_1091` `pow-sqr_binary64_1074` `distribute-lft-neg-out_binary64_1060` `distribute-rgt-out_binary64_1054` `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` `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` `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` `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` `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--l-_binary64_1039` `associate--r+_binary64_1037` `associate-+l-_binary64_1036` `associate-+r-_binary64_1035` `associate-+l+_binary64_1034`

Counts

465 → 335

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	836	11227
1	2030	10856
2	5166	10856

prune683.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	332	3	335
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	336	11	347

Error

3.5b

Counts

347 → 11

Compiler

Compiled 7496 to 4186 computations (44.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.6b	(/.f64 M (/.f64 2 (/.f64 D d)))
5.6b	(/.f64 M (/.f64 2 (/.f64 D d)))
6.0b	(*.f64 h (/.f64 M (/.f64 2 (/.f64 D d))))
6.4b	(/.f64 (.f64 (.f64 h (/.f64 M (/.f64 2 (/.f64 D d)))) (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) (/.f64 2 2))) l)

rewrite2.9s (10.5%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

1131×	`times-frac_binary64_1107`
541×	`add-sqr-sqrt_binary64_1123`
527×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
213×	`add-exp-log_binary64_1139`
137×	`associate-r_binary64_1041`
115×	`div-exp_binary64_1152`
91×	`associate-/r*_binary64_1045`
63×	`add-cbrt-cube_binary64_1137`
58×	`prod-exp_binary64_1150`
48×	`div-inv_binary64_1098`
30×	`cbrt-undiv_binary64_1135`
20×	`pow-exp_binary64_1169`
14×	`associate-/r/_binary64_1047`
13×	`cbrt-unprod_binary64_1134`
7×	`associate-/l*_binary64_1046`
6×	`pow1_binary64_1162`
5×	`pow-to-exp_binary64_1170`
4×	`add-log-exp_binary64_1140` `unswap-sqr_binary64_1069`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-l_binary64_1042`
2×	`associate-*r/_binary64_1043`
1×	`associate-l/_binary64_1044` `associate-/l/_binary64_1048` `pow-prod-down_binary64_1172` `-commutative_binary64_1032`

Counts

4 → 609

Calls

4 calls:

55.0ms	(/.f64 (.f64 (.f64 h (/.f64 M (/.f64 2 (/.f64 D d)))) (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) (/.f64 2 2))) l)
42.0ms	(*.f64 h (/.f64 M (/.f64 2 (/.f64 D d))))
20.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))
13.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))

Compiler

Compiled 25128 to 14307 computations (43.1% saved)

series1.5s (5.5%)

Error

3.5b

Counts

4 → 45

Calls

4 calls:

827.0ms	(/.f64 (.f64 (.f64 h (/.f64 M (/.f64 2 (/.f64 D d)))) (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) (/.f64 2 2))) l)
315.0ms	(*.f64 h (/.f64 M (/.f64 2 (/.f64 D d))))
187.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))
184.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))

Compiler

Compiled 2446 to 2235 computations (8.6% saved)

simplify313.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

704×	`associate-/r/_binary64_1047`
552×	`associate-/l*_binary64_1046`
496×	`associate-*l/_binary64_1044`
476×	`associate-/l/_binary64_1048`
370×	`associate-/r*_binary64_1045`
367×	`times-frac_binary64_1107`
154×	`*-commutative_binary64_1032`
140×	`associate-*r/_binary64_1043`
40×	`sub-neg_binary64_1094`
25×	`associate--l+_binary64_1038`
24×	`associate-l_binary64_1042`
20×	`associate-+l+_binary64_1034`
13×	`remove-double-div_binary64_1077` `associate-r_binary64_1041`
12×	`log-div_binary64_1188` `swap-sqr_binary64_1068`
11×	`/-rgt-identity_binary64_1092`
10×	`neg-mul-1_binary64_1097` `neg-sub0_binary64_1096` `sqr-pow_binary64_1073`
9×	`log-prod_binary64_1187` `+-commutative_binary64_1031`
8×	`distribute-neg-frac_binary64_1065` `distribute-rgt-neg-in_binary64_1059` `distribute-lft-neg-in_binary64_1058`
7×	`cube-unmult_binary64_1138` `unswap-sqr_binary64_1069`
6×	`exp-prod_binary64_1153`
5×	`*-rgt-identity_binary64_1091`
4×	`pow-plus_binary64_1164` `unpow1_binary64_1159`
3×	`unpow2_binary64_1166` `cancel-sign-sub-inv_binary64_1067` `distribute-neg-in_binary64_1062` `associate-+r-_binary64_1035`
2×	`distribute-rgt-out_binary64_1054` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050` `associate--r-_binary64_1040`
1×	`log-pow_binary64_1190` `log-rec_binary64_1189` `unpow1/2_binary64_1165` `1-exp_binary64_1145` `rem-sqrt-square_binary64_1114` `pow-sqr_binary64_1074` `distribute-rgt1-in_binary64_1057`
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` `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` `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` `div-sub_binary64_1106` `unsub-neg_binary64_1095` `mul-1-neg_binary64_1093` `-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_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-lft-neg-out_binary64_1060` `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--l-_binary64_1039` `associate--r+_binary64_1037` `associate-+l-_binary64_1036` `associate-+r+_binary64_1033`

Counts

654 → 486

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	705	15507
1	1604	14970
2	4989	14970

prune1.2s (4.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	486	0	486
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	486	11	497

Error

3.5b

Counts

497 → 11

Compiler

Compiled 14518 to 7960 computations (45.2% saved)

regimes6.7s (24.3%)

Accuracy

Total 4.5b remaining (53.5%)

Threshold costs 0b (0%)

Compiler

Compiled 73049 to 67750 computations (7.3% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64_1032`
6×	`sub-neg_binary64_1094` `+-commutative_binary64_1031`
5×	`neg-mul-1_binary64_1097` `neg-sub0_binary64_1096`
2×	`distribute-neg-frac_binary64_1065` `distribute-rgt-neg-in_binary64_1059` `distribute-lft-neg-in_binary64_1058`
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-inv_binary64_1067` `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-lft-neg-out_binary64_1060`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	36
1	24	36
2	30	36
3	40	36
4	49	36
5	56	36
6	60	36
7	61	36
8	60	36

end9.0ms (0%)

Compiler: Compiled 72 to 60 computations (16.7% saved)

sample2.2s (8%)

Algorithm

1×

intervals

Results

609.0ms	8000×	body	128	valid
246.0ms	3159×	body	128	nan
114.0ms	1420×	body	128	invalid

Compiler

Compiled 268 to 275 computations (-2.6% saved)

Details

analyze2.9s (10.4%)

sample65.0ms (0.2%)

simplify44.0ms (0.2%)

prune2.0ms (0%)

localize14.0ms (0.1%)

rewrite309.0ms (1.1%)

series2.2s (8%)

simplify160.0ms (0.6%)

prune198.0ms (0.7%)

localize18.0ms (0.1%)

rewrite288.0ms (1%)

series2.0s (7.2%)

simplify100.0ms (0.4%)

prune118.0ms (0.4%)

localize19.0ms (0.1%)

rewrite1.5s (5.3%)

series2.0s (7.2%)

simplify230.0ms (0.8%)

prune683.0ms (2.5%)

localize18.0ms (0.1%)

rewrite2.9s (10.5%)

series1.5s (5.5%)

simplify313.0ms (1.1%)

prune1.2s (4.4%)

regimes6.7s (24.3%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end9.0ms (0%)

sample2.2s (8%)

Profiling