Details

analyze507.0ms (3.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample22.0ms (0.2%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify152.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

2× *-commutative_binary64_1032 +-commutative_binary64_1031

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 unpow2_binary64_1166 unpow1/2_binary64_1165 pow-plus_binary64_1164 exp-to-pow_binary64_1163 pow-base-1_binary64_1161 unpow0_binary64_1160 unpow1_binary64_1159 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 1-exp_binary64_1145 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-sqrt-square_binary64_1114 rem-square-sqrt_binary64_1113 times-frac_binary64_1107 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 *-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 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 sqr-pow_binary64_1073 difference-of-sqr--1_binary64_1072 difference-of-sqr-1_binary64_1071 difference-of-squares_binary64_1070 unswap-sqr_binary64_1069 swap-sqr_binary64_1068 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-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-/l/_binary64_1048 associate-/r/_binary64_1047 associate-/l*_binary64_1046 associate-/r*_binary64_1045 associate-*l/_binary64_1044 associate-*r/_binary64_1043 associate-*l*_binary64_1042 associate-*r*_binary64_1041 associate--r-_binary64_1040 associate--l-_binary64_1039 associate--l+_binary64_1038 associate--r+_binary64_1037 associate-+l-_binary64_1036 associate-+r-_binary64_1035 associate-+l+_binary64_1034 associate-+r+_binary64_1033

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	18	30

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

22.6b

Counts

1 → 1

Compiler

Compiled 15 to 11 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.0b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
22.1b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite93.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

22.4b

Rules

11×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
9×	`times-frac_binary64_1107`
7×	`add-log-exp_binary64_1140`
5×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
4×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
3×	`pow1_binary64_1162` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `sum-log_binary64_1192` `+-commutative_binary64_1031`
1×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098`

Counts

3 → 53

Calls

3 calls:

8.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Compiler

Compiled 1469 to 193 computations (86.9% saved)

series815.0ms (6.1%)

Error

4.5b

Counts

3 → 60

Calls

3 calls:

433.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
211.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
125.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

Compiler

Compiled 2046 to 1284 computations (37.2% saved)

simplify282.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

777×	`distribute-rgt-in_binary64_1051`
420×	`associate-l_binary64_1042`
350×	`unswap-sqr_binary64_1069`
345×	`associate-r_binary64_1041`
295×	`cancel-sign-sub-inv_binary64_1067`
221×	`distribute-rgt-out_binary64_1054`
173×	`distribute-rgt-neg-in_binary64_1059`
148×	`distribute-lft-in_binary64_1050`
142×	`distribute-lft-neg-in_binary64_1058`
124×	`distribute-lft-out_binary64_1052` `*-commutative_binary64_1032`
102×	`sqr-pow_binary64_1073`
97×	`associate-/l*_binary64_1046`
94×	`sub-neg_binary64_1094`
89×	`times-frac_binary64_1107`
63×	`associate-/l/_binary64_1048`
62×	`pow-sqr_binary64_1074` `associate-*r/_binary64_1043`
61×	`associate-/r*_binary64_1045`
59×	`distribute-lft-neg-out_binary64_1060`
54×	`associate-*l/_binary64_1044`
50×	`associate-/r/_binary64_1047`
45×	`neg-sub0_binary64_1096`
41×	`div-sub_binary64_1106` `neg-mul-1_binary64_1097`
40×	`unsub-neg_binary64_1095`
37×	`distribute-rgt-out--_binary64_1055`
36×	`difference-of-squares_binary64_1070`
32×	`distribute-rgt-neg-out_binary64_1061` `associate-+l+_binary64_1034`
29×	`pow-plus_binary64_1164` `+-commutative_binary64_1031`
28×	`associate-+r+_binary64_1033`
25×	`exp-prod_binary64_1153`
24×	`cube-prod_binary64_1129`
18×	`*-lft-identity_binary64_1090` `associate-+r-_binary64_1035`
17×	`/-rgt-identity_binary64_1092`
16×	`distribute-neg-in_binary64_1062` `associate-+l-_binary64_1036`
15×	`+-rgt-identity_binary64_1086`
14×	`cube-unmult_binary64_1138` `distribute-neg-out_binary64_1063` `distribute-lft-out--_binary64_1053`
12×	`unpow3_binary64_1167` `sub0-neg_binary64_1088` `distribute-neg-frac_binary64_1065`
11×	`prod-exp_binary64_1150` `*-rgt-identity_binary64_1091` `swap-sqr_binary64_1068`
10×	`log-div_binary64_1188` `log-prod_binary64_1187`
9×	`div-exp_binary64_1152`
6×	`cube-mult_binary64_1131`
5×	`cube-div_binary64_1130`
4×	`cancel-sign-sub_binary64_1066` `distribute-rgt1-in_binary64_1057`
3×	`rec-exp_binary64_1151`
2×	`unpow2_binary64_1166` `unpow1_binary64_1159` `exp-sqrt_binary64_1154` `associate--l+_binary64_1038` `associate--r+_binary64_1037`
1×	`log-pow_binary64_1190` `log-rec_binary64_1189` `exp-lft-sqr_binary64_1156` `exp-diff_binary64_1149` `1-exp_binary64_1145` `rem-log-exp_binary64_1142` `*-inverses_binary64_1081` `rgt-mult-inverse_binary64_1078` `distribute-frac-neg_binary64_1064` `associate--l-_binary64_1039`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1364` `erf-erfc_binary64_1363` `erf-odd_binary64_1362` `if-if-and-not_binary64_1361` `if-if-and_binary64_1360` `if-if-or-not_binary64_1359` `if-if-or_binary64_1358` `if-not_binary64_1357` `if-same_binary64_1356` `if-false_binary64_1355` `if-true_binary64_1354` `not-gte_binary64_1353` `not-lte_binary64_1352` `not-gt_binary64_1351` `not-lt_binary64_1350` `gte-same_binary64_1349` `lte-same_binary64_1348` `gt-same_binary64_1347` `lt-same_binary64_1346` `sinh---cosh_binary64_1293` `sinh-+-cosh_binary64_1292` `sinh-cosh_binary64_1291` `tanh-def-c_binary64_1290` `tanh-def-b_binary64_1289` `tanh-def-a_binary64_1288` `cosh-def_binary64_1287` `sinh-def_binary64_1286` `tan-neg_binary64_1233` `cos-neg_binary64_1232` `sin-neg_binary64_1231` `tan-0_binary64_1230` `cos-0_binary64_1229` `sin-0_binary64_1228` `hang-m-tan_binary64_1227` `hang-p-tan_binary64_1226` `hang-m0-tan_binary64_1225` `hang-p0-tan_binary64_1224` `hang-0m-tan_binary64_1223` `hang-0p-tan_binary64_1222` `tan-+PI/2_binary64_1221` `tan-+PI_binary64_1220` `tan-PI_binary64_1219` `tan-PI/3_binary64_1218` `tan-PI/4_binary64_1217` `tan-PI/6_binary64_1216` `cos-+PI/2_binary64_1215` `cos-+PI_binary64_1214` `cos-PI_binary64_1213` `cos-PI/2_binary64_1212` `cos-PI/3_binary64_1211` `cos-PI/4_binary64_1210` `cos-PI/6_binary64_1209` `sin-+PI/2_binary64_1208` `sin-+PI_binary64_1207` `sin-PI_binary64_1206` `sin-PI/2_binary64_1205` `sin-PI/3_binary64_1204` `sin-PI/4_binary64_1203` `sin-PI/6_binary64_1202` `sub-1-sin_binary64_1201` `sub-1-cos_binary64_1200` `-1-add-sin_binary64_1199` `-1-add-cos_binary64_1198` `1-sub-sin_binary64_1197` `1-sub-cos_binary64_1196` `cos-sin-sum_binary64_1195` `log-E_binary64_1191` `pow-base-0_binary64_1185` `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-cbrt_binary64_1155` `exp-neg_binary64_1148` `exp-sum_binary64_1147` `e-exp-1_binary64_1146` `exp-1-e_binary64_1144` `exp-0_binary64_1143` `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` `rem-sqrt-square_binary64_1114` `rem-square-sqrt_binary64_1113` `mul-1-neg_binary64_1093` `remove-double-neg_binary64_1089` `--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` `difference-of-sqr-1_binary64_1071` `distribute-lft1-in_binary64_1056` `count-2_binary64_1049` `associate--r-_binary64_1040`

Counts

113 → 198

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	110	2791
1	317	2603
2	1074	2603
3	2798	2603

prune266.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	193	5	198
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	194	5	199

Error

5.5b

Counts

199 → 5

Compiler

Compiled 5279 to 2096 computations (60.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.2b	(*.f64 (/.f64 y.im (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) x.im)
3.4b	(*.f64 (/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) x.re)
15.7b	(/.f64 y.im (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
16.3b	(/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite373.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

5.5b

Rules

100×	`*-un-lft-identity_binary64_1101`
62×	`times-frac_binary64_1107`
54×	`add-sqr-sqrt_binary64_1123`
44×	`add-cube-cbrt_binary64_1136`
42×	`associate-l_binary64_1042`
28×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
18×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
10×	`associate-/r*_binary64_1045`
8×	`pow1_binary64_1162` `associate-/r/_binary64_1047`
6×	`associate-/l_binary64_1046` `associate-r*_binary64_1041`
4×	`div-exp_binary64_1152` `add-log-exp_binary64_1140` `cbrt-undiv_binary64_1135` `div-inv_binary64_1098` `flip3-+_binary64_1104` `flip-+_binary64_1075` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `unswap-sqr_binary64_1069`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `pow-prod-down_binary64_1172` `associate-l/_binary64_1044` `-commutative_binary64_1032`

Counts

4 → 154

Calls

4 calls:

14.0ms	(*.f64 (/.f64 y.im (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) x.im)
13.0ms	(*.f64 (/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) x.re)
12.0ms	(/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
9.0ms	(/.f64 y.im (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 5148 to 3420 computations (33.6% saved)

series846.0ms (6.3%)

Error

5.5b

Counts

4 → 54

Calls

4 calls:

329.0ms	(*.f64 (/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) x.re)
194.0ms	(*.f64 (/.f64 y.im (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) x.im)
185.0ms	(/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
69.0ms	(/.f64 y.im (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 3408 to 2534 computations (25.6% saved)

simplify576.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

582×	`associate-/l*_binary64_1046`
463×	`times-frac_binary64_1107`
280×	`*-commutative_binary64_1032`
255×	`associate-/r*_binary64_1045`
253×	`unswap-sqr_binary64_1069`
185×	`associate-/r/_binary64_1047`
183×	`associate-/l/_binary64_1048`
157×	`sub-neg_binary64_1094`
156×	`sqr-pow_binary64_1073`
123×	`cancel-sign-sub-inv_binary64_1067`
120×	`associate-l_binary64_1042`
106×	`associate-*l/_binary64_1044`
99×	`associate-r_binary64_1041`
93×	`pow-sqr_binary64_1074`
71×	`neg-mul-1_binary64_1097` `distribute-rgt-in_binary64_1051`
70×	`neg-sub0_binary64_1096`
65×	`div-sub_binary64_1106`
60×	`associate-*r/_binary64_1043`
58×	`log-prod_binary64_1187` `distribute-lft-in_binary64_1050`
56×	`log-div_binary64_1188` `cube-prod_binary64_1129` `/-rgt-identity_binary64_1092` `distribute-rgt-neg-in_binary64_1059`
54×	`unsub-neg_binary64_1095`
52×	`cube-div_binary64_1130` `distribute-lft-neg-in_binary64_1058`
51×	`difference-of-squares_binary64_1070`
47×	`+-commutative_binary64_1031`
45×	`pow-plus_binary64_1164`
40×	`*-rgt-identity_binary64_1091` `associate-+l-_binary64_1036`
37×	`distribute-neg-frac_binary64_1065`
35×	`associate-+l+_binary64_1034`
34×	`exp-prod_binary64_1153`
28×	`associate-+r-_binary64_1035`
27×	`associate-+r+_binary64_1033`
25×	`associate--l+_binary64_1038`
19×	`log-pow_binary64_1190`
18×	`*-lft-identity_binary64_1090` `sub0-neg_binary64_1088` `+-rgt-identity_binary64_1086`
16×	`div-exp_binary64_1152` `prod-exp_binary64_1150`
15×	`associate--r+_binary64_1037`
14×	`unpow3_binary64_1167` `swap-sqr_binary64_1068`
13×	`log-rec_binary64_1189`
12×	`cube-unmult_binary64_1138` `distribute-rgt-out_binary64_1054`
9×	`cube-mult_binary64_1131` `distribute-rgt-out--_binary64_1055`
8×	`remove-double-div_binary64_1077` `distribute-neg-in_binary64_1062`
7×	`pow-base-1_binary64_1161` `distribute-lft-neg-out_binary64_1060`
6×	`exp-lft-sqr_binary64_1156`
4×	`rec-exp_binary64_1151` `distribute-lft-out_binary64_1052` `associate--l-_binary64_1039`
3×	`unpow2_binary64_1166` `distribute-rgt-neg-out_binary64_1061` `distribute-lft-out--_binary64_1053`
2×	`unpow1_binary64_1159` `rem-sqrt-square_binary64_1114` `remove-double-neg_binary64_1089` `mul0-rgt_binary64_1084` `mul0-lft_binary64_1083` `div0_binary64_1082`
1×	`exp-sqrt_binary64_1154` `exp-diff_binary64_1149` `1-exp_binary64_1145` `exp-1-e_binary64_1144` `rem-log-exp_binary64_1142` `*-inverses_binary64_1081` `rgt-mult-inverse_binary64_1078`
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` `unpow1/2_binary64_1165` `exp-to-pow_binary64_1163` `unpow0_binary64_1160` `unpow-1_binary64_1158` `exp-lft-cube_binary64_1157` `exp-cbrt_binary64_1155` `exp-neg_binary64_1148` `exp-sum_binary64_1147` `e-exp-1_binary64_1146` `exp-0_binary64_1143` `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` `rem-square-sqrt_binary64_1113` `mul-1-neg_binary64_1093` `--rgt-identity_binary64_1087` `+-lft-identity_binary64_1085` `+-inverses_binary64_1080` `lft-mult-inverse_binary64_1079` `difference-of-sqr--1_binary64_1072` `difference-of-sqr-1_binary64_1071` `cancel-sign-sub_binary64_1066` `distribute-frac-neg_binary64_1064` `distribute-neg-out_binary64_1063` `distribute-rgt1-in_binary64_1057` `distribute-lft1-in_binary64_1056` `count-2_binary64_1049` `associate--r-_binary64_1040`

Counts

208 → 423

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	5205
1	537	4821
2	1723	4770
3	4200	4770

prune1.0s (7.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	421	2	423
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	422	6	428

Error

5.5b

Counts

428 → 6

Compiler

Compiled 14683 to 9633 computations (34.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.4b	(*.f64 (/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) x.re)
16.3b	(/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
25.6b	(sqrt.f64 (+.f64 (pow.f64 y.im 2) (pow.f64 y.re 2)))
25.6b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite547.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

5.5b

Rules

62×	`*-un-lft-identity_binary64_1101`
33×	`add-sqr-sqrt_binary64_1123`
31×	`times-frac_binary64_1107`
26×	`add-cube-cbrt_binary64_1136`
21×	`associate-l_binary64_1042`
18×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
11×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
10×	`sqrt-prod_binary64_1117`
8×	`pow1_binary64_1162`
5×	`associate-/r*_binary64_1045`
4×	`add-log-exp_binary64_1140` `flip3-+_binary64_1104` `sqrt-div_binary64_1118` `flip-+_binary64_1075` `associate-/r/_binary64_1047`
3×	`associate-/l_binary64_1046` `associate-r*_binary64_1041`
2×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `div-inv_binary64_1098` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `unswap-sqr_binary64_1069`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `pow-prod-down_binary64_1172` `associate-l/_binary64_1044` `-commutative_binary64_1032`

Counts

4 → 111

Calls

4 calls:

13.0ms	(*.f64 (/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) x.re)
9.0ms	(/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.im 2) (pow.f64 y.re 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 4770 to 3362 computations (29.5% saved)

series965.0ms (7.2%)

Error

5.5b

Counts

4 → 69

Calls

4 calls:

356.0ms	(*.f64 (/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) x.re)
186.0ms	(/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
152.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
144.0ms	(sqrt.f64 (+.f64 (pow.f64 y.im 2) (pow.f64 y.re 2)))

Compiler

Compiled 5913 to 4450 computations (24.7% saved)

simplify320.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

516×	`times-frac_binary64_1107`
450×	`associate-/l*_binary64_1046`
420×	`associate-*l/_binary64_1044`
303×	`associate-*r/_binary64_1043`
272×	`associate-/r*_binary64_1045`
172×	`cancel-sign-sub-inv_binary64_1067`
148×	`associate-/r/_binary64_1047`
140×	`associate-/l/_binary64_1048`
94×	`unswap-sqr_binary64_1069`
91×	`distribute-rgt-in_binary64_1051`
86×	`associate-l_binary64_1042`
82×	`distribute-rgt-neg-in_binary64_1059`
80×	`associate-r_binary64_1041`
71×	`distribute-lft-neg-in_binary64_1058` `distribute-lft-in_binary64_1050`
70×	`sub-neg_binary64_1094`
60×	`sqr-pow_binary64_1073`
59×	`*-commutative_binary64_1032`
53×	`distribute-neg-frac_binary64_1065`
47×	`associate-+l-_binary64_1036`
42×	`associate-+l+_binary64_1034`
40×	`associate-+r-_binary64_1035`
36×	`neg-mul-1_binary64_1097` `neg-sub0_binary64_1096` `pow-sqr_binary64_1074`
35×	`difference-of-squares_binary64_1070`
34×	`+-commutative_binary64_1031`
32×	`associate-+r+_binary64_1033`
27×	`associate--l+_binary64_1038`
21×	`associate--r+_binary64_1037`
18×	`log-div_binary64_1188` `pow-plus_binary64_1164`
17×	`log-prod_binary64_1187`
16×	`div-exp_binary64_1152` `prod-exp_binary64_1150` `*-rgt-identity_binary64_1091`
15×	`cube-prod_binary64_1129`
14×	`unsub-neg_binary64_1095`
13×	`cube-div_binary64_1130` `distribute-lft-neg-out_binary64_1060`
12×	`exp-prod_binary64_1153` `distribute-neg-in_binary64_1062`
11×	`swap-sqr_binary64_1068` `distribute-rgt-out--_binary64_1055` `distribute-rgt-out_binary64_1054`
10×	`/-rgt-identity_binary64_1092`
7×	`cube-unmult_binary64_1138`
6×	`log-pow_binary64_1190` `unpow3_binary64_1167` `*-lft-identity_binary64_1090`
5×	`distribute-lft-out--_binary64_1053`
4×	`rec-exp_binary64_1151` `rem-sqrt-square_binary64_1114` `distribute-lft-out_binary64_1052`
3×	`unpow2_binary64_1166` `pow-base-1_binary64_1161` `cube-mult_binary64_1131` `div-sub_binary64_1106` `distribute-rgt-neg-out_binary64_1061`
2×	`unpow1_binary64_1159` `rem-square-sqrt_binary64_1113` `associate--l-_binary64_1039`
1×	`log-rec_binary64_1189` `exp-sqrt_binary64_1154` `1-exp_binary64_1145` `exp-1-e_binary64_1144` `rem-log-exp_binary64_1142` `mul-1-neg_binary64_1093` `sub0-neg_binary64_1088` `+-rgt-identity_binary64_1086` `*-inverses_binary64_1081` `cancel-sign-sub_binary64_1066` `count-2_binary64_1049` `associate--r-_binary64_1040`
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` `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-diff_binary64_1149` `exp-neg_binary64_1148` `exp-sum_binary64_1147` `e-exp-1_binary64_1146` `exp-0_binary64_1143` `rem-exp-log_binary64_1141` `cube-neg_binary64_1128` `rem-3cbrt-rft_binary64_1127` `rem-3cbrt-lft_binary64_1126` `rem-cbrt-cube_binary64_1125` `rem-cube-cbrt_binary64_1124` `sqr-abs_binary64_1116` `sqr-neg_binary64_1115` `remove-double-neg_binary64_1089` `--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` `rgt-mult-inverse_binary64_1078` `remove-double-div_binary64_1077` `difference-of-sqr--1_binary64_1072` `difference-of-sqr-1_binary64_1071` `distribute-frac-neg_binary64_1064` `distribute-neg-out_binary64_1063` `distribute-rgt1-in_binary64_1057` `distribute-lft1-in_binary64_1056`

Counts

180 → 197

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	4176
1	447	3962
2	1518	3911

prune617.0ms (4.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	197	6	203

Error

5.5b

Counts

203 → 6

Compiler

Compiled 8776 to 6157 computations (29.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

16.3b	(/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.5b	(cbrt.f64 (+.f64 (pow.f64 y.im 2) (pow.f64 y.re 2)))
26.5b	(cbrt.f64 (+.f64 (pow.f64 y.im 2) (pow.f64 y.re 2)))
26.5b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite326.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

5.5b

Rules

45×	`*-un-lft-identity_binary64_1101`
17×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123`
15×	`cbrt-prod_binary64_1132` `times-frac_binary64_1107`
14×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `cbrt-div_binary64_1133`
5×	`associate-/r*_binary64_1045`
4×	`pow1_binary64_1162` `add-log-exp_binary64_1140` `flip3-+_binary64_1104` `flip-+_binary64_1075`
3×	`pow1/3_binary64_1183` `associate-/l*_binary64_1046`
2×	`associate-/r/_binary64_1047`
1×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098`

Counts

4 → 82

Calls

4 calls:

12.0ms	(/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
7.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
7.0ms	(cbrt.f64 (+.f64 (pow.f64 y.im 2) (pow.f64 y.re 2)))
7.0ms	(cbrt.f64 (+.f64 (pow.f64 y.im 2) (pow.f64 y.re 2)))

Compiler

Compiled 4826 to 3253 computations (32.6% saved)

series1.1s (8.3%)

Error

5.5b

Counts

4 → 54

Calls

4 calls:

258.0ms	(cbrt.f64 (+.f64 (pow.f64 y.im 2) (pow.f64 y.re 2)))
255.0ms	(cbrt.f64 (+.f64 (pow.f64 y.im 2) (pow.f64 y.re 2)))
252.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
195.0ms	(/.f64 y.re (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 7257 to 5348 computations (26.3% saved)

simplify311.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

136 → 230

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	3056
1	288	2990
2	998	2966
3	3153	2966

prune1.1s (8.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	230	6	236

Error

5.5b

Counts

236 → 6

Compiler

Compiled 13586 to 9159 computations (32.6% saved)

regimes1.1s (7.9%)

Accuracy

Total 8.8b remaining (65.8%)

Threshold costs 0b (0%)

Compiler

Compiled 8556 to 5446 computations (36.3% saved)

bsearch112.0ms (0.8%)

Steps

Iters	Range		Point
9	6.481960614973319e+121	3.975844796144771e+127	1.177941737878767e+124
9	1.6645669551164747e-174	4.5457658723462674e-167	4.463976884807298e-167
9	-7.642351285570655e-135	-2.785547969133938e-142	-1.4208537250093686e-139
5	-2.1328240910461253e+68	-9.632018697239982e+67	-2.1127488063854356e+68

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64_1031`
3×	`*-commutative_binary64_1032`
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` `1-exp_binary64_1145` `exp-1-e_binary64_1144` `exp-0_binary64_1143` `sqr-abs_binary64_1116` `sqr-neg_binary64_1115` `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` `-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-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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	196
1	46	196

Proof

(if real (<= f64 (y re) -211274880638543564078360177947673237718966821915581326454142500077568) (/ f64 (x re) (y re)) (if real (<= f64 (y re) -1905053384146909/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (+ f64 (* f64 (/ f64 (/ f64 (y im) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (sqrt f64 (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2)))) (x im)) (* f64 (/ f64 (y re) (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2))) (x re))) (if real (<= f64 (y re) 5927469306442483/132784498204191774672397051638117156832398279431757980799861034550100889965213060684790625566307321417222332371561625253836644834413176809852379994691646837985957817708848304757932032) (+ f64 (/ f64 (x im) (y im)) (/ f64 (* f64 (y re) (x re)) (pow f64 (y im) 2))) (if real (<= f64 (y re) 11779417378787670592083809455456373656733530111164153131944231133993335346523911322726652807291912644492823010779443387957248) (+ f64 (* f64 (/ f64 (/ f64 (y im) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (sqrt f64 (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2)))) (x im)) (=> (* f64 (/ f64 (y re) (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2))) (x re)))) (+ f64 (/ f64 (x re) (y re)) (/ f64 (y im) (/ f64 (pow f64 (y re) 2) (x im))))))))
*-commutative_binary64_1032 =>
(if real (<= f64 (y re) -211274880638543564078360177947673237718966821915581326454142500077568) (/ f64 (x re) (y re)) (if real (<= f64 (y re) -1905053384146909/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (+ f64 (* f64 (/ f64 (/ f64 (y im) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (sqrt f64 (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2)))) (x im)) (=> (* f64 (/ f64 (y re) (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2))) (x re)))) (if real (<= f64 (y re) 5927469306442483/132784498204191774672397051638117156832398279431757980799861034550100889965213060684790625566307321417222332371561625253836644834413176809852379994691646837985957817708848304757932032) (+ f64 (/ f64 (x im) (y im)) (/ f64 (* f64 (y re) (x re)) (pow f64 (y im) 2))) (if real (<= f64 (y re) 11779417378787670592083809455456373656733530111164153131944231133993335346523911322726652807291912644492823010779443387957248) (+ f64 (* f64 (/ f64 (/ f64 (y im) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (sqrt f64 (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2)))) (x im)) (* f64 (x re) (/ f64 (y re) (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2))))) (+ f64 (/ f64 (x re) (y re)) (/ f64 (y im) (/ f64 (pow f64 (y re) 2) (x im))))))))
*-commutative_binary64_1032 =>
(if real (<= f64 (y re) -211274880638543564078360177947673237718966821915581326454142500077568) (/ f64 (x re) (y re)) (if real (<= f64 (y re) -1905053384146909/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (+ f64 (* f64 (/ f64 (/ f64 (y im) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (sqrt f64 (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2)))) (x im)) (* f64 (x re) (/ f64 (y re) (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2))))) (if real (<= f64 (y re) 5927469306442483/132784498204191774672397051638117156832398279431757980799861034550100889965213060684790625566307321417222332371561625253836644834413176809852379994691646837985957817708848304757932032) (+ f64 (/ f64 (x im) (y im)) (/ f64 (* f64 (y re) (x re)) (pow f64 (y im) 2))) (if real (<= f64 (y re) 11779417378787670592083809455456373656733530111164153131944231133993335346523911322726652807291912644492823010779443387957248) (+ f64 (* f64 (/ f64 (/ f64 (y im) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (sqrt f64 (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2)))) (x im)) (* f64 (x re) (/ f64 (y re) (=> (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2)))))) (+ f64 (/ f64 (x re) (y re)) (/ f64 (y im) (/ f64 (pow f64 (y re) 2) (x im))))))))
+-commutative_binary64_1031 =>
(if real (<= f64 (y re) -211274880638543564078360177947673237718966821915581326454142500077568) (/ f64 (x re) (y re)) (if real (<= f64 (y re) -1905053384146909/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (+ f64 (* f64 (/ f64 (/ f64 (y im) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (sqrt f64 (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2)))) (x im)) (* f64 (x re) (/ f64 (y re) (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2))))) (if real (<= f64 (y re) 5927469306442483/132784498204191774672397051638117156832398279431757980799861034550100889965213060684790625566307321417222332371561625253836644834413176809852379994691646837985957817708848304757932032) (+ f64 (/ f64 (x im) (y im)) (/ f64 (* f64 (y re) (x re)) (pow f64 (y im) 2))) (if real (<= f64 (y re) 11779417378787670592083809455456373656733530111164153131944231133993335346523911322726652807291912644492823010779443387957248) (+ f64 (* f64 (/ f64 (/ f64 (y im) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (sqrt f64 (=> (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2))))) (x im)) (* f64 (x re) (/ f64 (y re) (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2))))) (+ f64 (/ f64 (x re) (y re)) (/ f64 (y im) (/ f64 (pow f64 (y re) 2) (x im))))))))
+-commutative_binary64_1031 =>
(if real (<= f64 (y re) -211274880638543564078360177947673237718966821915581326454142500077568) (/ f64 (x re) (y re)) (if real (<= f64 (y re) -1905053384146909/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (+ f64 (* f64 (/ f64 (/ f64 (y im) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (sqrt f64 (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2)))) (x im)) (* f64 (x re) (/ f64 (y re) (=> (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2)))))) (if real (<= f64 (y re) 5927469306442483/132784498204191774672397051638117156832398279431757980799861034550100889965213060684790625566307321417222332371561625253836644834413176809852379994691646837985957817708848304757932032) (+ f64 (/ f64 (x im) (y im)) (/ f64 (* f64 (y re) (x re)) (pow f64 (y im) 2))) (if real (<= f64 (y re) 11779417378787670592083809455456373656733530111164153131944231133993335346523911322726652807291912644492823010779443387957248) (+ f64 (* f64 (/ f64 (/ f64 (y im) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (x im)) (* f64 (x re) (/ f64 (y re) (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2))))) (+ f64 (/ f64 (x re) (y re)) (/ f64 (y im) (/ f64 (pow f64 (y re) 2) (x im))))))))
+-commutative_binary64_1031 =>
(if real (<= f64 (y re) -211274880638543564078360177947673237718966821915581326454142500077568) (/ f64 (x re) (y re)) (if real (<= f64 (y re) -1905053384146909/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (+ f64 (* f64 (/ f64 (/ f64 (y im) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (sqrt f64 (=> (+ f64 (pow f64 (y re) 2) (pow f64 (y im) 2))))) (x im)) (* f64 (x re) (/ f64 (y re) (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2))))) (if real (<= f64 (y re) 5927469306442483/132784498204191774672397051638117156832398279431757980799861034550100889965213060684790625566307321417222332371561625253836644834413176809852379994691646837985957817708848304757932032) (+ f64 (/ f64 (x im) (y im)) (/ f64 (* f64 (y re) (x re)) (pow f64 (y im) 2))) (if real (<= f64 (y re) 11779417378787670592083809455456373656733530111164153131944231133993335346523911322726652807291912644492823010779443387957248) (+ f64 (* f64 (/ f64 (/ f64 (y im) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (x im)) (* f64 (x re) (/ f64 (y re) (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2))))) (+ f64 (/ f64 (x re) (y re)) (/ f64 (y im) (/ f64 (pow f64 (y re) 2) (x im))))))))
+-commutative_binary64_1031 =>
(if real (<= f64 (y re) -211274880638543564078360177947673237718966821915581326454142500077568) (/ f64 (x re) (y re)) (if real (<= f64 (y re) -1905053384146909/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (+ f64 (* f64 (/ f64 (/ f64 (y im) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (x im)) (* f64 (x re) (/ f64 (y re) (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2))))) (if real (<= f64 (y re) 5927469306442483/132784498204191774672397051638117156832398279431757980799861034550100889965213060684790625566307321417222332371561625253836644834413176809852379994691646837985957817708848304757932032) (+ f64 (/ f64 (x im) (y im)) (/ f64 (* f64 (y re) (x re)) (pow f64 (y im) 2))) (if real (<= f64 (y re) 11779417378787670592083809455456373656733530111164153131944231133993335346523911322726652807291912644492823010779443387957248) (+ f64 (* f64 (/ f64 (/ f64 (y im) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (sqrt f64 (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2)))) (x im)) (* f64 (x re) (/ f64 (y re) (+ f64 (pow f64 (y im) 2) (pow f64 (y re) 2))))) (+ f64 (/ f64 (x re) (y re)) (/ f64 (y im) (/ f64 (pow f64 (y re) 2) (x im))))))))

end0.0ms (0%)

sample1.9s (14.1%)

Algorithm

1×

intervals

Results

323.0ms	8000×	body	128	valid
15.0ms	415×	body	128	invalid

Compiler

Compiled 1788 to 1151 computations (35.6% saved)

Details

analyze507.0ms (3.8%)

sample22.0ms (0.2%)

simplify152.0ms (1.1%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite93.0ms (0.7%)

series815.0ms (6.1%)

simplify282.0ms (2.1%)

prune266.0ms (2%)

localize12.0ms (0.1%)

rewrite373.0ms (2.8%)

series846.0ms (6.3%)

simplify576.0ms (4.3%)

prune1.0s (7.6%)

localize16.0ms (0.1%)

rewrite547.0ms (4.1%)

series965.0ms (7.2%)

simplify320.0ms (2.4%)

prune617.0ms (4.6%)

localize22.0ms (0.2%)

rewrite326.0ms (2.4%)

series1.1s (8.3%)

simplify311.0ms (2.3%)

prune1.1s (8.1%)

regimes1.1s (7.9%)

bsearch112.0ms (0.8%)

simplify13.0ms (0.1%)

end0.0ms (0%)

sample1.9s (14.1%)

Profiling