Details

analyze2.8s (12.2%)

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)

sample68.0ms (0.3%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
8.0ms	40×	body	128	invalid
7.0ms	91×	body	128	nan

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify42.0ms (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

14.6b

Counts

1 → 1

Compiler

Compiled 18 to 18 computations (0% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.3b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
6.0b	(/.f64 (.f64 M D) (.f64 2 d))
11.8b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite253.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

7.7b

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:

13.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
13.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
7.0ms	(/.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 3444 to 1962 computations (43% saved)

series2.6s (11.3%)

Error

7.0b

Counts

4 → 66

Calls

4 calls:

976.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
825.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
503.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
199.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4487 to 3912 computations (12.8% saved)

simplify159.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

300×	`times-frac_binary64_1107`
293×	`associate-l_binary64_1042`
258×	`associate-r_binary64_1041`
235×	`associate-/l*_binary64_1046`
211×	`distribute-neg-frac_binary64_1065`
199×	`log-prod_binary64_1187`
184×	`associate-/r*_binary64_1045`
176×	`cancel-sign-sub-inv_binary64_1067`
172×	`associate-*r/_binary64_1043`
163×	`*-commutative_binary64_1032`
137×	`associate-*l/_binary64_1044`
134×	`log-div_binary64_1188`
133×	`unswap-sqr_binary64_1069`
73×	`cube-prod_binary64_1129`
68×	`neg-sub0_binary64_1096` `sqr-pow_binary64_1073`
66×	`swap-sqr_binary64_1068`
63×	`neg-mul-1_binary64_1097`
60×	`sub-neg_binary64_1094`
59×	`exp-prod_binary64_1153`
51×	`distribute-rgt-neg-in_binary64_1059`
45×	`distribute-lft-neg-in_binary64_1058`
40×	`+-commutative_binary64_1031`
39×	`cube-div_binary64_1130`
36×	`-rgt-identity_binary64_1091` `-lft-identity_binary64_1090`
22×	`log-pow_binary64_1190` `associate-/r/_binary64_1047`
19×	`associate-/l/_binary64_1048`
14×	`/-rgt-identity_binary64_1092`
12×	`associate--l+_binary64_1038`
9×	`unpow3_binary64_1167` `unsub-neg_binary64_1095`
8×	`unpow2_binary64_1166` `unpow1/2_binary64_1165` `unpow1_binary64_1159` `cube-unmult_binary64_1138` `associate-+l+_binary64_1034`
7×	`cube-mult_binary64_1131` `distribute-rgt-in_binary64_1051`
6×	`pow-plus_binary64_1164` `rem-sqrt-square_binary64_1114` `associate-+r-_binary64_1035`
5×	`mul-1-neg_binary64_1093` `pow-sqr_binary64_1074` `distribute-lft-in_binary64_1050` `associate--r+_binary64_1037`
4×	`exp-sqrt_binary64_1154` `rem-square-sqrt_binary64_1113` `distribute-neg-in_binary64_1062`
3×	`distribute-rgt-out_binary64_1054`
2×	`distribute-lft-neg-out_binary64_1060` `distribute-rgt1-in_binary64_1057` `distribute-lft-out_binary64_1052` `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-neg-out_binary64_1061` `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`

Counts

182 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	300	4606
1	780	4319
2	3371	4318
3	4839	4318
4	5056	4318

prune217.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	129	9	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	130	9	139

Error

5.2b

Counts

139 → 9

Compiler

Compiled 3814 to 2044 computations (46.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.3b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
4.8b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
6.0b	(/.f64 (.f64 M D) (.f64 2 d))
6.9b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)

rewrite189.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

4.5b

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` `unpow-prod-down_binary64_1180` `sqrt-prod_binary64_1117`
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` `unpow2_binary64_1166` `sqr-pow_binary64_1073` `sqrt-div_binary64_1118` `difference-of-squares_binary64_1070`
1×	`*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `distribute-lft-out--_binary64_1053` `rem-sqrt-square_binary64_1114`

Counts

4 → 99

Calls

4 calls:

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

Compiler

Compiled 2731 to 1689 computations (38.2% saved)

series2.2s (9.4%)

Error

4.8b

Counts

4 → 55

Calls

4 calls:

831.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
555.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
506.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
199.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3627 to 3235 computations (10.8% saved)

simplify98.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

823×	`associate-/r/_binary64_1047`
275×	`times-frac_binary64_1107`
221×	`associate-/l*_binary64_1046`
208×	`distribute-rgt-neg-in_binary64_1059`
196×	`distribute-lft-neg-in_binary64_1058`
178×	`distribute-neg-frac_binary64_1065`
168×	`associate-l_binary64_1042`
159×	`associate-r_binary64_1041`
158×	`associate-/r*_binary64_1045`
125×	`unswap-sqr_binary64_1069`
105×	`cancel-sign-sub-inv_binary64_1067`
101×	`associate-*r/_binary64_1043`
97×	`associate-*l/_binary64_1044`
93×	`*-commutative_binary64_1032`
71×	`log-prod_binary64_1187`
63×	`swap-sqr_binary64_1068`
62×	`log-div_binary64_1188`
61×	`sub-neg_binary64_1094`
60×	`sqr-pow_binary64_1073`
52×	`exp-prod_binary64_1153`
51×	`cube-prod_binary64_1129`
50×	`neg-sub0_binary64_1096`
48×	`cube-div_binary64_1130`
47×	`neg-mul-1_binary64_1097`
36×	`distribute-rgt-in_binary64_1051`
30×	`distribute-lft-in_binary64_1050`
28×	`+-commutative_binary64_1031`
26×	`associate-/l/_binary64_1048`
20×	`*-rgt-identity_binary64_1091`
19×	`*-lft-identity_binary64_1090`
15×	`associate--l+_binary64_1038`
13×	`distribute-lft-neg-out_binary64_1060`
12×	`/-rgt-identity_binary64_1092`
10×	`log-pow_binary64_1190`
9×	`unpow3_binary64_1167`
8×	`unpow2_binary64_1166` `unpow1/2_binary64_1165` `unpow1_binary64_1159` `distribute-rgt-neg-out_binary64_1061`
7×	`cube-unmult_binary64_1138` `cube-mult_binary64_1131`
6×	`pow-plus_binary64_1164` `rem-sqrt-square_binary64_1114` `unsub-neg_binary64_1095` `associate-+l+_binary64_1034`
5×	`distribute-rgt1-in_binary64_1057`
4×	`log-rec_binary64_1189` `exp-sqrt_binary64_1154` `rem-square-sqrt_binary64_1113` `pow-sqr_binary64_1074` `associate--r+_binary64_1037`
3×	`div-sub_binary64_1106` `mul-1-neg_binary64_1093` `distribute-lft-out_binary64_1052`
2×	`distribute-neg-in_binary64_1062` `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

154 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	3335
1	587	3149
2	2558	3140
3	5481	3140

prune141.0ms (0.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	96	12	108

Error

4.7b

Counts

108 → 12

Compiler

Compiled 2476 to 1475 computations (40.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.3b	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)))
4.2b	(/.f64 M (/.f64 2 (/.f64 D d)))
4.8b	(*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2))
6.9b	(/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)

rewrite1.1s (5%)

Algorithm

1×	rewrite-expression-head

Error

4.3b

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` `unpow2_binary64_1166` `sqr-pow_binary64_1073` `sqrt-div_binary64_1118` `difference-of-squares_binary64_1070`
1×	`*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `distribute-lft-out--_binary64_1053` `rem-sqrt-square_binary64_1114`

Counts

4 → 407

Calls

4 calls:

65.0ms	(*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2))
36.0ms	(/.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 13175 to 7612 computations (42.2% saved)

series2.1s (9.2%)

Error

4.6b

Counts

4 → 55

Calls

4 calls:

832.0ms	(/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)
527.0ms	(*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2))
480.0ms	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)))
193.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))

Compiler

Compiled 3627 to 3235 computations (10.8% saved)

simplify221.0ms (1%)

Algorithm

1×	egg-herbie

Rules

723×	`associate-*l/_binary64_1044`
552×	`associate-/r/_binary64_1047`
395×	`associate-/l/_binary64_1048`
316×	`associate-/r*_binary64_1045`
272×	`associate-/l*_binary64_1046`
262×	`sqr-pow_binary64_1073`
176×	`times-frac_binary64_1107`
167×	`*-commutative_binary64_1032`
125×	`unpow2_binary64_1166`
124×	`unpow1_binary64_1159`
115×	`swap-sqr_binary64_1068`
30×	`sub-neg_binary64_1094`
28×	`distribute-rgt-neg-in_binary64_1059`
26×	`distribute-neg-frac_binary64_1065`
24×	`neg-sub0_binary64_1096`
23×	`distribute-lft-neg-in_binary64_1058`
22×	`neg-mul-1_binary64_1097`
21×	`associate-*r/_binary64_1043`
18×	`cancel-sign-sub-inv_binary64_1067`
13×	`log-div_binary64_1188` `remove-double-div_binary64_1077`
12×	`unswap-sqr_binary64_1069`
11×	`/-rgt-identity_binary64_1092` `associate-l_binary64_1042` `+-commutative_binary64_1031`
10×	`log-prod_binary64_1187`
9×	`associate-r_binary64_1041`
8×	`exp-prod_binary64_1153` `cube-div_binary64_1130`
7×	`unpow3_binary64_1167` `rem-square-sqrt_binary64_1113` `associate--l+_binary64_1038`
5×	`cube-unmult_binary64_1138` `cube-mult_binary64_1131`
4×	`cube-prod_binary64_1129` `rem-sqrt-square_binary64_1114`
3×	`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` `pow-plus_binary64_1164` `*-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` `*-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

462 → 339

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	852	11307
1	2087	10942
2	5314	10942

prune809.0ms (3.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	336	3	339
Fresh	2	8	10
Picked	1	0	1
Done	1	0	1
Total	340	11	351

Error

4.3b

Counts

351 → 11

Compiler

Compiled 9810 to 5340 computations (45.6% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.9b	(/.f64 (.f64 (.f64 h (pow.f64 (.f64 (.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 (/.f64 D d)) (cbrt.f64 (/.f64 D d)))) 2)) (pow.f64 (/.f64 (cbrt.f64 M) (/.f64 2 (cbrt.f64 (/.f64 D d)))) 2)) l)
12.2b	(cbrt.f64 (/.f64 D d))
12.2b	(cbrt.f64 (/.f64 D d))
12.2b	(cbrt.f64 (/.f64 D d))

rewrite382.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

4.3b

Rules

212×	`add-exp-log_binary64_1139`
115×	`prod-exp_binary64_1150`
65×	`div-exp_binary64_1152`
49×	`pow-exp_binary64_1169`
39×	`cbrt-prod_binary64_1132`
30×	`times-frac_binary64_1107`
27×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
13×	`add-cbrt-cube_binary64_1137` `pow-to-exp_binary64_1170`
4×	`pow1_binary64_1162` `add-log-exp_binary64_1140` `div-inv_binary64_1098`
3×	`pow1/3_binary64_1183` `cbrt-div_binary64_1133` `cbrt-undiv_binary64_1135` `cbrt-unprod_binary64_1134` `associate-/r*_binary64_1045`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l*_binary64_1046`

Counts

4 → 127

Calls

4 calls:

88.0ms	(/.f64 (.f64 (.f64 h (pow.f64 (.f64 (.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 (/.f64 D d)) (cbrt.f64 (/.f64 D d)))) 2)) (pow.f64 (/.f64 (cbrt.f64 M) (/.f64 2 (cbrt.f64 (/.f64 D d)))) 2)) l)
3.0ms	(cbrt.f64 (/.f64 D d))
3.0ms	(cbrt.f64 (/.f64 D d))
3.0ms	(cbrt.f64 (/.f64 D d))

Compiler

Compiled 5970 to 2283 computations (61.8% saved)

series1.9s (8.5%)

Error

4.3b

Counts

4 → 33

Calls

4 calls:

972.0ms	(/.f64 (.f64 (.f64 h (pow.f64 (.f64 (.f64 (cbrt.f64 M) (cbrt.f64 M)) (*.f64 (cbrt.f64 (/.f64 D d)) (cbrt.f64 (/.f64 D d)))) 2)) (pow.f64 (/.f64 (cbrt.f64 M) (/.f64 2 (cbrt.f64 (/.f64 D d)))) 2)) l)
315.0ms	(cbrt.f64 (/.f64 D d))
301.0ms	(cbrt.f64 (/.f64 D d))
295.0ms	(cbrt.f64 (/.f64 D d))

Compiler

Compiled 3483 to 2658 computations (23.7% saved)

simplify169.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

819×	`associate-/r*_binary64_1045`
530×	`associate-*l/_binary64_1044`
412×	`associate-/l/_binary64_1048`
324×	`associate-/r/_binary64_1047`
234×	`log-div_binary64_1188`
124×	`associate-l_binary64_1042`
121×	`associate-/l*_binary64_1046`
108×	`associate-r_binary64_1041`
95×	`times-frac_binary64_1107`
73×	`*-commutative_binary64_1032`
68×	`unswap-sqr_binary64_1069`
67×	`sub-neg_binary64_1094`
58×	`log-prod_binary64_1187`
50×	`+-commutative_binary64_1031`
41×	`distribute-lft-neg-in_binary64_1058`
40×	`swap-sqr_binary64_1068`
39×	`sqr-pow_binary64_1073`
38×	`distribute-rgt-neg-in_binary64_1059` `associate-*r/_binary64_1043`
36×	`distribute-rgt-in_binary64_1051`
33×	`associate-+l+_binary64_1034`
30×	`distribute-lft-in_binary64_1050` `associate--l+_binary64_1038`
27×	`cube-prod_binary64_1129`
24×	`cube-div_binary64_1130`
21×	`neg-mul-1_binary64_1097` `neg-sub0_binary64_1096`
18×	`*-rgt-identity_binary64_1091` `cancel-sign-sub-inv_binary64_1067`
16×	`exp-prod_binary64_1153` `exp-sum_binary64_1147` `distribute-neg-frac_binary64_1065`
11×	`log-pow_binary64_1190` `cube-unmult_binary64_1138` `div-sub_binary64_1106`
10×	`log-rec_binary64_1189` `exp-diff_binary64_1149` `unsub-neg_binary64_1095` `/-rgt-identity_binary64_1092`
8×	`distribute-rgt-neg-out_binary64_1061`
7×	`distribute-lft-neg-out_binary64_1060`
6×	`associate-+r+_binary64_1033`
5×	`unpow2_binary64_1166` `unpow1/2_binary64_1165` `unpow1_binary64_1159` `mul-1-neg_binary64_1093` `*-lft-identity_binary64_1090` `pow-sqr_binary64_1074` `distribute-neg-in_binary64_1062`
4×	`pow-plus_binary64_1164` `exp-neg_binary64_1148` `distribute-neg-out_binary64_1063` `distribute-rgt-out_binary64_1054` `distribute-lft-out_binary64_1052` `associate-+l-_binary64_1036`
3×	`unpow1/3_binary64_1168` `exp-to-pow_binary64_1163` `associate--r-_binary64_1040`
2×	`rem-sqrt-square_binary64_1114` `remove-double-neg_binary64_1089` `distribute-frac-neg_binary64_1064` `count-2_binary64_1049` `associate--l-_binary64_1039` `associate-+r-_binary64_1035`
1×	`unpow3_binary64_1167` `1-exp_binary64_1145` `cube-mult_binary64_1131` `rem-3cbrt-lft_binary64_1126` `rem-cube-cbrt_binary64_1124` `associate--r+_binary64_1037`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1364` `erf-erfc_binary64_1363` `erf-odd_binary64_1362` `if-if-and-not_binary64_1361` `if-if-and_binary64_1360` `if-if-or-not_binary64_1359` `if-if-or_binary64_1358` `if-not_binary64_1357` `if-same_binary64_1356` `if-false_binary64_1355` `if-true_binary64_1354` `not-gte_binary64_1353` `not-lte_binary64_1352` `not-gt_binary64_1351` `not-lt_binary64_1350` `gte-same_binary64_1349` `lte-same_binary64_1348` `gt-same_binary64_1347` `lt-same_binary64_1346` `sinh---cosh_binary64_1293` `sinh-+-cosh_binary64_1292` `sinh-cosh_binary64_1291` `tanh-def-c_binary64_1290` `tanh-def-b_binary64_1289` `tanh-def-a_binary64_1288` `cosh-def_binary64_1287` `sinh-def_binary64_1286` `tan-neg_binary64_1233` `cos-neg_binary64_1232` `sin-neg_binary64_1231` `tan-0_binary64_1230` `cos-0_binary64_1229` `sin-0_binary64_1228` `hang-m-tan_binary64_1227` `hang-p-tan_binary64_1226` `hang-m0-tan_binary64_1225` `hang-p0-tan_binary64_1224` `hang-0m-tan_binary64_1223` `hang-0p-tan_binary64_1222` `tan-+PI/2_binary64_1221` `tan-+PI_binary64_1220` `tan-PI_binary64_1219` `tan-PI/3_binary64_1218` `tan-PI/4_binary64_1217` `tan-PI/6_binary64_1216` `cos-+PI/2_binary64_1215` `cos-+PI_binary64_1214` `cos-PI_binary64_1213` `cos-PI/2_binary64_1212` `cos-PI/3_binary64_1211` `cos-PI/4_binary64_1210` `cos-PI/6_binary64_1209` `sin-+PI/2_binary64_1208` `sin-+PI_binary64_1207` `sin-PI_binary64_1206` `sin-PI/2_binary64_1205` `sin-PI/3_binary64_1204` `sin-PI/4_binary64_1203` `sin-PI/6_binary64_1202` `sub-1-sin_binary64_1201` `sub-1-cos_binary64_1200` `-1-add-sin_binary64_1199` `-1-add-cos_binary64_1198` `1-sub-sin_binary64_1197` `1-sub-cos_binary64_1196` `cos-sin-sum_binary64_1195` `log-E_binary64_1191` `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` `exp-sqrt_binary64_1154` `div-exp_binary64_1152` `rec-exp_binary64_1151` `prod-exp_binary64_1150` `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-cbrt-cube_binary64_1125` `sqr-abs_binary64_1116` `sqr-neg_binary64_1115` `rem-square-sqrt_binary64_1113` `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-rgt1-in_binary64_1057` `distribute-lft1-in_binary64_1056` `distribute-rgt-out--_binary64_1055` `distribute-lft-out--_binary64_1053`

Counts

160 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	5267
1	408	4637
2	1476	4361
3	4893	4361
4	5202	4361

prune176.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	102	11	113

Error

4.3b

Counts

113 → 11

Compiler

Compiled 3708 to 1584 computations (57.3% saved)

regimes3.2s (14%)

Accuracy

Total 4.1b remaining (49.8%)

Threshold costs 0b (0%)

Compiler

Compiled 33545 to 30022 computations (10.5% saved)

bsearch5.0ms (0%)

Compiler: Compiled 15 to 16 computations (-6.7% saved)

simplify29.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	170
1	86	170
2	117	170
3	149	170
4	176	170
5	190	170
6	196	170
7	197	170
8	196	170

Compiler

Compiled 222 to 142 computations (36% saved)

end0.0ms (0%)

sample3.9s (17.1%)

Algorithm

1×

intervals

Results

655.0ms	8000×	body	128	valid
258.0ms	3111×	body	128	nan
112.0ms	1354×	body	128	invalid

Compiler

Compiled 2123 to 1859 computations (12.4% saved)

Iter	Nodes	Cost
0	54	170
1	86	170
2	117	170
3	149	170
4	176	170
5	190	170
6	196	170
7	197	170
8	196	170

Iter	Nodes	Cost
0	54	170
1	86	170
2	117	170
3	149	170
4	176	170
5	190	170
6	196	170
7	197	170
8	196	170

Details

analyze2.8s (12.2%)

sample68.0ms (0.3%)

simplify42.0ms (0.2%)

prune2.0ms (0%)

localize16.0ms (0.1%)

rewrite253.0ms (1.1%)

series2.6s (11.3%)

simplify159.0ms (0.7%)

prune217.0ms (0.9%)

localize16.0ms (0.1%)

rewrite189.0ms (0.8%)

series2.2s (9.4%)

simplify98.0ms (0.4%)

prune141.0ms (0.6%)

localize16.0ms (0.1%)

rewrite1.1s (5%)

series2.1s (9.2%)

simplify221.0ms (1%)

prune809.0ms (3.5%)

localize30.0ms (0.1%)

rewrite382.0ms (1.7%)

series1.9s (8.5%)

simplify169.0ms (0.7%)

prune176.0ms (0.8%)

regimes3.2s (14%)

bsearch5.0ms (0%)

simplify29.0ms (0.1%)

end0.0ms (0%)

sample3.9s (17.1%)

Profiling

Iter	Nodes	Cost
0	54	170
1	86	170
2	117	170
3	149	170
4	176	170
5	190	170
6	196	170
7	197	170
8	196	170