Details

analyze36.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 18 to 11 computations (38.9% saved)

sample25.0ms (0.3%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true
0.0ms	2×	pre	128	false

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify174.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

624×	`neg-mul-1_binary64_1097`
414×	`sub-neg_binary64_1094`
381×	`distribute-frac-neg_binary64_1064`
364×	`div-sub_binary64_1106`
297×	`unsub-neg_binary64_1095`
254×	`*-commutative_binary64_1032`
253×	`times-frac_binary64_1107`
204×	`neg-sub0_binary64_1096`
190×	`cancel-sign-sub-inv_binary64_1067` `distribute-rgt-in_binary64_1051`
178×	`associate-/l*_binary64_1046`
174×	`associate-/r/_binary64_1047`
173×	`associate-*l/_binary64_1044`
171×	`distribute-lft-in_binary64_1050`
143×	`distribute-neg-frac_binary64_1065`
137×	`cube-prod_binary64_1129`
134×	`distribute-neg-out_binary64_1063`
131×	`associate-/l/_binary64_1048`
114×	`associate-l_binary64_1042`
103×	`associate-*r/_binary64_1043`
97×	`distribute-lft-neg-out_binary64_1060`
96×	`distribute-rgt-neg-out_binary64_1061`
91×	`distribute-rgt-neg-in_binary64_1059` `associate-+l-_binary64_1036`
89×	`distribute-rgt-out_binary64_1054`
83×	`associate--r+_binary64_1037`
79×	`associate-/r*_binary64_1045`
78×	`associate-+l+_binary64_1034`
70×	`associate-r_binary64_1041`
66×	`distribute-lft-neg-in_binary64_1058`
63×	`cube-div_binary64_1130`
62×	`div0_binary64_1082`
60×	`swap-sqr_binary64_1068`
57×	`associate-+r+_binary64_1033`
55×	`associate--l+_binary64_1038`
50×	`remove-double-neg_binary64_1089`
48×	`distribute-rgt-out--_binary64_1055`
45×	`sqr-neg_binary64_1115` `+-commutative_binary64_1031`
43×	`sub0-neg_binary64_1088`
38×	`associate-+r-_binary64_1035`
34×	`mul0-rgt_binary64_1084`
33×	`mul0-lft_binary64_1083`
31×	`cube-neg_binary64_1128`
29×	`unpow3_binary64_1167` `cube-mult_binary64_1131`
27×	`distribute-neg-in_binary64_1062`
24×	`/-rgt-identity_binary64_1092`
21×	`associate--r-_binary64_1040`
19×	`associate--l-_binary64_1039`
16×	`distribute-lft-out_binary64_1052`
13×	`*-rgt-identity_binary64_1091`
11×	`+-lft-identity_binary64_1085` `cancel-sign-sub_binary64_1066`
10×	`--rgt-identity_binary64_1087` `unswap-sqr_binary64_1069`
8×	`mul-1-neg_binary64_1093`
7×	`*-lft-identity_binary64_1090` `+-rgt-identity_binary64_1086` `sqr-pow_binary64_1073`
6×	`distribute-lft-out--_binary64_1053`
5×	`distribute-rgt1-in_binary64_1057`
4×	`remove-double-div_binary64_1077`
3×	`+-inverses_binary64_1080`
2×	`cube-unmult_binary64_1138` `*-inverses_binary64_1081` `lft-mult-inverse_binary64_1079` `difference-of-sqr--1_binary64_1072` `difference-of-squares_binary64_1070` `distribute-lft1-in_binary64_1056`
1×	`unpow2_binary64_1166` `pow-plus_binary64_1164` `1-exp_binary64_1145` `difference-of-sqr-1_binary64_1071`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1364` `erf-erfc_binary64_1363` `erf-odd_binary64_1362` `if-if-and-not_binary64_1361` `if-if-and_binary64_1360` `if-if-or-not_binary64_1359` `if-if-or_binary64_1358` `if-not_binary64_1357` `if-same_binary64_1356` `if-false_binary64_1355` `if-true_binary64_1354` `not-gte_binary64_1353` `not-lte_binary64_1352` `not-gt_binary64_1351` `not-lt_binary64_1350` `gte-same_binary64_1349` `lte-same_binary64_1348` `gt-same_binary64_1347` `lt-same_binary64_1346` `sinh---cosh_binary64_1293` `sinh-+-cosh_binary64_1292` `sinh-cosh_binary64_1291` `tanh-def-c_binary64_1290` `tanh-def-b_binary64_1289` `tanh-def-a_binary64_1288` `cosh-def_binary64_1287` `sinh-def_binary64_1286` `tan-neg_binary64_1233` `cos-neg_binary64_1232` `sin-neg_binary64_1231` `tan-0_binary64_1230` `cos-0_binary64_1229` `sin-0_binary64_1228` `hang-m-tan_binary64_1227` `hang-p-tan_binary64_1226` `hang-m0-tan_binary64_1225` `hang-p0-tan_binary64_1224` `hang-0m-tan_binary64_1223` `hang-0p-tan_binary64_1222` `tan-+PI/2_binary64_1221` `tan-+PI_binary64_1220` `tan-PI_binary64_1219` `tan-PI/3_binary64_1218` `tan-PI/4_binary64_1217` `tan-PI/6_binary64_1216` `cos-+PI/2_binary64_1215` `cos-+PI_binary64_1214` `cos-PI_binary64_1213` `cos-PI/2_binary64_1212` `cos-PI/3_binary64_1211` `cos-PI/4_binary64_1210` `cos-PI/6_binary64_1209` `sin-+PI/2_binary64_1208` `sin-+PI_binary64_1207` `sin-PI_binary64_1206` `sin-PI/2_binary64_1205` `sin-PI/3_binary64_1204` `sin-PI/4_binary64_1203` `sin-PI/6_binary64_1202` `sub-1-sin_binary64_1201` `sub-1-cos_binary64_1200` `-1-add-sin_binary64_1199` `-1-add-cos_binary64_1198` `1-sub-sin_binary64_1197` `1-sub-cos_binary64_1196` `cos-sin-sum_binary64_1195` `log-E_binary64_1191` `log-pow_binary64_1190` `log-rec_binary64_1189` `log-div_binary64_1188` `log-prod_binary64_1187` `pow-base-0_binary64_1185` `unpow1/3_binary64_1168` `unpow1/2_binary64_1165` `exp-to-pow_binary64_1163` `pow-base-1_binary64_1161` `unpow0_binary64_1160` `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` `exp-1-e_binary64_1144` `exp-0_binary64_1143` `rem-log-exp_binary64_1142` `rem-exp-log_binary64_1141` `rem-3cbrt-rft_binary64_1127` `rem-3cbrt-lft_binary64_1126` `rem-cbrt-cube_binary64_1125` `rem-cube-cbrt_binary64_1124` `sqr-abs_binary64_1116` `rem-sqrt-square_binary64_1114` `rem-square-sqrt_binary64_1113` `rgt-mult-inverse_binary64_1078` `pow-sqr_binary64_1074` `count-2_binary64_1049`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	22	17
2	54	17
3	115	17
4	245	17
5	646	17
6	1944	17
7	3229	17
8	4346	17
9	4836	17

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

14.8b

Counts

2 → 2

Compiler

Compiled 35 to 26 computations (25.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 a a) (.f64 b b))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
14.4b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

rewrite64.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

8×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
7×	`add-sqr-sqrt_binary64_1123`
6×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
5×	`add-log-exp_binary64_1140`
4×	`pow1_binary64_1162` `times-frac_binary64_1107` `associate-/l*_binary64_1046`
3×	`difference-of-squares_binary64_1070` `sqrt-prod_binary64_1117`
2×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `flip--_binary64_1076`
1×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `frac-2neg_binary64_1112` `div-sub_binary64_1106` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/r*_binary64_1045` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `diff-log_binary64_1193` `sub-neg_binary64_1094` `cancel-sign-sub-inv_binary64_1067`

Counts

3 → 52

Calls

3 calls:

8.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
4.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 1164 to 244 computations (79% saved)

series352.0ms (4.9%)

Error

0.4b

Counts

3 → 30

Calls

3 calls:

159.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
93.0ms	(-.f64 (.f64 a a) (.f64 b b))
78.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 870 to 747 computations (14.1% saved)

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

390×	`times-frac_binary64_1107`
377×	`unswap-sqr_binary64_1069`
279×	`div-sub_binary64_1106`
260×	`associate-l_binary64_1042`
249×	`associate-/l*_binary64_1046`
225×	`associate-r_binary64_1041`
214×	`distribute-rgt-in_binary64_1051`
206×	`distribute-lft-in_binary64_1050`
145×	`associate-/r*_binary64_1045`
143×	`associate-*l/_binary64_1044`
106×	`associate-*r/_binary64_1043`
92×	`exp-prod_binary64_1153`
74×	`sub-neg_binary64_1094`
73×	`*-commutative_binary64_1032`
72×	`unsub-neg_binary64_1095`
62×	`sqr-pow_binary64_1073`
49×	`exp-sum_binary64_1147`
48×	`associate-/l/_binary64_1048`
46×	`difference-of-squares_binary64_1070`
44×	`neg-sub0_binary64_1096`
40×	`cube-prod_binary64_1129`
38×	`cancel-sign-sub-inv_binary64_1067`
37×	`associate-/r/_binary64_1047`
34×	`neg-mul-1_binary64_1097`
29×	`log-prod_binary64_1187`
28×	`distribute-rgt-neg-in_binary64_1059`
27×	`log-div_binary64_1188` `+-commutative_binary64_1031`
23×	`cube-div_binary64_1130` `distribute-lft-neg-in_binary64_1058`
20×	`*-rgt-identity_binary64_1091`
19×	`*-lft-identity_binary64_1090`
15×	`exp-diff_binary64_1149`
14×	`distribute-lft-neg-out_binary64_1060`
12×	`unpow3_binary64_1167`
11×	`cube-unmult_binary64_1138` `pow-sqr_binary64_1074` `associate-+l+_binary64_1034`
10×	`mul0-rgt_binary64_1084` `mul0-lft_binary64_1083` `distribute-neg-in_binary64_1062`
9×	`distribute-rgt-neg-out_binary64_1061`
7×	`cube-mult_binary64_1131` `distribute-neg-frac_binary64_1065` `distribute-rgt-out_binary64_1054` `associate-+l-_binary64_1036`
6×	`pow-plus_binary64_1164` `mul-1-neg_binary64_1093` `sub0-neg_binary64_1088` `associate--r+_binary64_1037`
5×	`rem-sqrt-square_binary64_1114` `+-rgt-identity_binary64_1086` `associate-+r-_binary64_1035` `associate-+r+_binary64_1033`
4×	`remove-double-neg_binary64_1089` `swap-sqr_binary64_1068`
3×	`div0_binary64_1082` `distribute-lft-out_binary64_1052`
2×	`log-pow_binary64_1190` `unpow2_binary64_1166` `unpow1/2_binary64_1165` `unpow1_binary64_1159` `exp-neg_binary64_1148` `sqr-neg_binary64_1115` `*-inverses_binary64_1081` `associate--r-_binary64_1040` `associate--l+_binary64_1038`
1×	`div-exp_binary64_1152` `1-exp_binary64_1145` `exp-1-e_binary64_1144` `cube-neg_binary64_1128` `rem-square-sqrt_binary64_1113` `/-rgt-identity_binary64_1092` `difference-of-sqr-1_binary64_1071` `count-2_binary64_1049`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1364` `erf-erfc_binary64_1363` `erf-odd_binary64_1362` `if-if-and-not_binary64_1361` `if-if-and_binary64_1360` `if-if-or-not_binary64_1359` `if-if-or_binary64_1358` `if-not_binary64_1357` `if-same_binary64_1356` `if-false_binary64_1355` `if-true_binary64_1354` `not-gte_binary64_1353` `not-lte_binary64_1352` `not-gt_binary64_1351` `not-lt_binary64_1350` `gte-same_binary64_1349` `lte-same_binary64_1348` `gt-same_binary64_1347` `lt-same_binary64_1346` `sinh---cosh_binary64_1293` `sinh-+-cosh_binary64_1292` `sinh-cosh_binary64_1291` `tanh-def-c_binary64_1290` `tanh-def-b_binary64_1289` `tanh-def-a_binary64_1288` `cosh-def_binary64_1287` `sinh-def_binary64_1286` `tan-neg_binary64_1233` `cos-neg_binary64_1232` `sin-neg_binary64_1231` `tan-0_binary64_1230` `cos-0_binary64_1229` `sin-0_binary64_1228` `hang-m-tan_binary64_1227` `hang-p-tan_binary64_1226` `hang-m0-tan_binary64_1225` `hang-p0-tan_binary64_1224` `hang-0m-tan_binary64_1223` `hang-0p-tan_binary64_1222` `tan-+PI/2_binary64_1221` `tan-+PI_binary64_1220` `tan-PI_binary64_1219` `tan-PI/3_binary64_1218` `tan-PI/4_binary64_1217` `tan-PI/6_binary64_1216` `cos-+PI/2_binary64_1215` `cos-+PI_binary64_1214` `cos-PI_binary64_1213` `cos-PI/2_binary64_1212` `cos-PI/3_binary64_1211` `cos-PI/4_binary64_1210` `cos-PI/6_binary64_1209` `sin-+PI/2_binary64_1208` `sin-+PI_binary64_1207` `sin-PI_binary64_1206` `sin-PI/2_binary64_1205` `sin-PI/3_binary64_1204` `sin-PI/4_binary64_1203` `sin-PI/6_binary64_1202` `sub-1-sin_binary64_1201` `sub-1-cos_binary64_1200` `-1-add-sin_binary64_1199` `-1-add-cos_binary64_1198` `1-sub-sin_binary64_1197` `1-sub-cos_binary64_1196` `cos-sin-sum_binary64_1195` `log-E_binary64_1191` `log-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` `exp-sqrt_binary64_1154` `rec-exp_binary64_1151` `prod-exp_binary64_1150` `e-exp-1_binary64_1146` `exp-0_binary64_1143` `rem-log-exp_binary64_1142` `rem-exp-log_binary64_1141` `rem-3cbrt-rft_binary64_1127` `rem-3cbrt-lft_binary64_1126` `rem-cbrt-cube_binary64_1125` `rem-cube-cbrt_binary64_1124` `sqr-abs_binary64_1116` `--rgt-identity_binary64_1087` `+-lft-identity_binary64_1085` `+-inverses_binary64_1080` `lft-mult-inverse_binary64_1079` `rgt-mult-inverse_binary64_1078` `remove-double-div_binary64_1077` `difference-of-sqr--1_binary64_1072` `cancel-sign-sub_binary64_1066` `distribute-frac-neg_binary64_1064` `distribute-neg-out_binary64_1063` `distribute-rgt1-in_binary64_1057` `distribute-lft1-in_binary64_1056` `distribute-rgt-out--_binary64_1055` `distribute-lft-out--_binary64_1053` `associate--l-_binary64_1039`

Counts

82 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1346
1	225	1203
2	660	1189
3	3365	1189
4	4937	1189

prune82.0ms (1.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	92	1	93

Error

0.0b

Counts

93 → 1

Compiler

Compiled 1782 to 570 computations (68% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
0.0b	(/.f64 a (/.f64 (-.f64 a b) a))
0.0b	(/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))
0.0b	(/.f64 (-.f64 a b) a)

rewrite589.0ms (8.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

890×	`times-frac_binary64_1107`
617×	`*-un-lft-identity_binary64_1101`
492×	`add-sqr-sqrt_binary64_1123`
369×	`add-cube-cbrt_binary64_1136`
84×	`associate-/r*_binary64_1045`
63×	`distribute-lft-out_binary64_1052`
61×	`difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053`
27×	`div-inv_binary64_1098`
20×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
12×	`associate-/l*_binary64_1046`
10×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
7×	`associate-/r/_binary64_1047`
5×	`pow1_binary64_1162`
4×	`add-log-exp_binary64_1140` `associate-/l/_binary64_1048`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `sqrt-prod_binary64_1117`
1×	`div-sub_binary64_1106` `flip3--_binary64_1105` `flip--_binary64_1076` `flip3-+_binary64_1104` `flip-+_binary64_1075` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114`

Counts

4 → 478

Calls

4 calls:

26.0ms	(/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))
9.0ms	(/.f64 a (/.f64 (-.f64 a b) a))
7.0ms	(/.f64 (-.f64 a b) a)
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))

Compiler

Compiled 13314 to 3223 computations (75.8% saved)

series426.0ms (5.9%)

Error

Counts

4 → 45

Calls

4 calls:

182.0ms	(/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))
80.0ms	(/.f64 (-.f64 a b) a)
77.0ms	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
55.0ms	(/.f64 a (/.f64 (-.f64 a b) a))

Compiler

Compiled 1350 to 974 computations (27.9% saved)

simplify464.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

748×	`associate-/r/_binary64_1047`
542×	`associate-/l/_binary64_1048`
484×	`associate-*r/_binary64_1043`
420×	`associate-*l/_binary64_1044`
309×	`associate-/r*_binary64_1045`
241×	`associate-/l*_binary64_1046`
176×	`associate-l_binary64_1042`
174×	`div-sub_binary64_1106`
156×	`times-frac_binary64_1107`
99×	`distribute-rgt-in_binary64_1051`
93×	`distribute-lft-in_binary64_1050`
88×	`*-rgt-identity_binary64_1091`
67×	`log-prod_binary64_1187`
63×	`log-div_binary64_1188`
58×	`cube-prod_binary64_1129`
57×	`exp-prod_binary64_1153`
52×	`unswap-sqr_binary64_1069`
48×	`sub-neg_binary64_1094`
47×	`cube-div_binary64_1130`
46×	`remove-double-div_binary64_1077`
39×	`distribute-neg-frac_binary64_1065`
33×	`*-lft-identity_binary64_1090`
31×	`neg-sub0_binary64_1096`
28×	`cancel-sign-sub-inv_binary64_1067`
25×	`neg-mul-1_binary64_1097` `swap-sqr_binary64_1068`
19×	`sqr-pow_binary64_1073`
16×	`/-rgt-identity_binary64_1092`
14×	`unpow3_binary64_1167`
13×	`log-rec_binary64_1189`
12×	`exp-sum_binary64_1147`
11×	`cube-unmult_binary64_1138` `*-commutative_binary64_1032`
10×	`cube-mult_binary64_1131` `+-commutative_binary64_1031`
8×	`unsub-neg_binary64_1095`
7×	`mul-1-neg_binary64_1093` `distribute-neg-in_binary64_1062`
6×	`exp-diff_binary64_1149`
4×	`log-pow_binary64_1190` `pow-plus_binary64_1164` `rem-sqrt-square_binary64_1114` `remove-double-neg_binary64_1089` `distribute-rgt-neg-in_binary64_1059` `associate-+r+_binary64_1033`
3×	`lft-mult-inverse_binary64_1079`
2×	`unpow2_binary64_1166` `unpow1/2_binary64_1165` `unpow1_binary64_1159` `sqr-neg_binary64_1115` `rem-square-sqrt_binary64_1113` `div0_binary64_1082` `*-inverses_binary64_1081` `difference-of-squares_binary64_1070` `distribute-lft-neg-in_binary64_1058` `associate--r-_binary64_1040`
1×	`1-exp_binary64_1145` `exp-1-e_binary64_1144` `cube-neg_binary64_1128` `rem-3cbrt-rft_binary64_1127` `rem-3cbrt-lft_binary64_1126` `pow-sqr_binary64_1074` `distribute-lft-neg-out_binary64_1060` `distribute-rgt-out--_binary64_1055` `distribute-rgt-out_binary64_1054` `associate-+r-_binary64_1035`
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-neg_binary64_1148` `e-exp-1_binary64_1146` `exp-0_binary64_1143` `rem-log-exp_binary64_1142` `rem-exp-log_binary64_1141` `rem-cbrt-cube_binary64_1125` `rem-cube-cbrt_binary64_1124` `sqr-abs_binary64_1116` `sub0-neg_binary64_1088` `--rgt-identity_binary64_1087` `+-rgt-identity_binary64_1086` `+-lft-identity_binary64_1085` `mul0-rgt_binary64_1084` `mul0-lft_binary64_1083` `+-inverses_binary64_1080` `rgt-mult-inverse_binary64_1078` `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-rgt-neg-out_binary64_1061` `distribute-rgt1-in_binary64_1057` `distribute-lft1-in_binary64_1056` `distribute-lft-out--_binary64_1053` `distribute-lft-out_binary64_1052` `count-2_binary64_1049` `associate-r_binary64_1041` `associate--l-_binary64_1039` `associate--l+_binary64_1038` `associate--r+_binary64_1037` `associate-+l-_binary64_1036` `associate-+l+_binary64_1034`

Counts

523 → 1931

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	593	15437
1	1326	14711
2	4469	14283
3	4571	14173
4	5044	14173

prune1.9s (26.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	1930	1	1931
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	1930	2	1932

Error

Counts

1932 → 2

Compiler

Compiled 53774 to 10606 computations (80.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (-.f64 1 (/.f64 b a))))))
0.0b	(/.f64 a (-.f64 1 (/.f64 b a)))
0.0b	(/.f64 (+.f64 a b) (/.f64 a (-.f64 1 (/.f64 b a))))

rewrite324.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

302×	`times-frac_binary64_1107`
261×	`add-sqr-sqrt_binary64_1123`
246×	`*-un-lft-identity_binary64_1101`
108×	`add-cube-cbrt_binary64_1136`
76×	`difference-of-squares_binary64_1070`
38×	`associate-/r*_binary64_1045`
31×	`distribute-lft-out_binary64_1052`
19×	`distribute-lft-out--_binary64_1053`
13×	`associate-/r/_binary64_1047`
10×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
7×	`div-inv_binary64_1098` `associate-/l*_binary64_1046`
6×	`flip3--_binary64_1105` `flip--_binary64_1076`
4×	`pow1_binary64_1162` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
3×	`add-log-exp_binary64_1140` `sqrt-prod_binary64_1117`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048`
1×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114`

Counts

3 → 233

Calls

3 calls:

18.0ms	(/.f64 (+.f64 a b) (/.f64 a (-.f64 1 (/.f64 b a))))
9.0ms	(/.f64 a (-.f64 1 (/.f64 b a)))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (-.f64 1 (/.f64 b a))))))

Compiler

Compiled 6338 to 2861 computations (54.9% saved)

series319.0ms (4.4%)

Error

Counts

3 → 33

Calls

3 calls:

169.0ms	(/.f64 (+.f64 a b) (/.f64 a (-.f64 1 (/.f64 b a))))
73.0ms	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (-.f64 1 (/.f64 b a))))))
53.0ms	(/.f64 a (-.f64 1 (/.f64 b a)))

Compiler

Compiled 978 to 727 computations (25.7% saved)

simplify246.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-/r/_binary64_1047`
535×	`times-frac_binary64_1107`
518×	`associate-/l*_binary64_1046`
384×	`distribute-rgt-in_binary64_1051`
350×	`distribute-lft-in_binary64_1050`
190×	`div-sub_binary64_1106`
188×	`associate-/l/_binary64_1048`
167×	`associate-*l/_binary64_1044`
137×	`*-commutative_binary64_1032`
85×	`associate-*r/_binary64_1043`
55×	`*-rgt-identity_binary64_1091`
47×	`distribute-lft-neg-out_binary64_1060`
43×	`distribute-rgt-neg-out_binary64_1061`
40×	`sub-neg_binary64_1094`
39×	`associate-r_binary64_1041`
37×	`cube-prod_binary64_1129`
34×	`associate-/r*_binary64_1045`
32×	`distribute-neg-frac_binary64_1065` `associate-l_binary64_1042`
28×	`distribute-rgt-neg-in_binary64_1059`
27×	`*-lft-identity_binary64_1090`
26×	`neg-sub0_binary64_1096` `cancel-sign-sub-inv_binary64_1067`
25×	`+-commutative_binary64_1031`
23×	`log-prod_binary64_1187` `neg-mul-1_binary64_1097`
22×	`log-div_binary64_1188` `cube-div_binary64_1130` `sqr-pow_binary64_1073` `unswap-sqr_binary64_1069`
19×	`distribute-lft-neg-in_binary64_1058`
14×	`exp-prod_binary64_1153`
13×	`associate-+l+_binary64_1034`
11×	`associate-+r+_binary64_1033`
10×	`unpow3_binary64_1167`
8×	`/-rgt-identity_binary64_1092` `swap-sqr_binary64_1068` `distribute-rgt-out_binary64_1054`
7×	`cube-unmult_binary64_1138` `distribute-neg-in_binary64_1062`
6×	`exp-sum_binary64_1147` `cube-mult_binary64_1131`
5×	`rem-sqrt-square_binary64_1114` `unsub-neg_binary64_1095` `remove-double-div_binary64_1077` `distribute-rgt1-in_binary64_1057`
4×	`mul-1-neg_binary64_1093` `distribute-rgt-out--_binary64_1055`
3×	`associate--r+_binary64_1037`
2×	`log-pow_binary64_1190` `unpow2_binary64_1166` `unpow1/2_binary64_1165` `pow-plus_binary64_1164` `unpow1_binary64_1159` `exp-diff_binary64_1149` `exp-neg_binary64_1148` `remove-double-neg_binary64_1089` `difference-of-squares_binary64_1070` `associate--r-_binary64_1040` `associate-+l-_binary64_1036`
1×	`log-rec_binary64_1189` `1-exp_binary64_1145` `cube-neg_binary64_1128` `sqr-neg_binary64_1115` `rem-square-sqrt_binary64_1113` `sub0-neg_binary64_1088` `div0_binary64_1082` `associate-+r-_binary64_1035`
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` `e-exp-1_binary64_1146` `exp-1-e_binary64_1144` `exp-0_binary64_1143` `rem-log-exp_binary64_1142` `rem-exp-log_binary64_1141` `rem-3cbrt-rft_binary64_1127` `rem-3cbrt-lft_binary64_1126` `rem-cbrt-cube_binary64_1125` `rem-cube-cbrt_binary64_1124` `sqr-abs_binary64_1116` `--rgt-identity_binary64_1087` `+-rgt-identity_binary64_1086` `+-lft-identity_binary64_1085` `mul0-rgt_binary64_1084` `mul0-lft_binary64_1083` `*-inverses_binary64_1081` `+-inverses_binary64_1080` `lft-mult-inverse_binary64_1079` `rgt-mult-inverse_binary64_1078` `pow-sqr_binary64_1074` `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-lft1-in_binary64_1056` `distribute-lft-out--_binary64_1053` `distribute-lft-out_binary64_1052` `count-2_binary64_1049` `associate--l-_binary64_1039` `associate--l+_binary64_1038`

Counts

266 → 637

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	289	7525
1	630	7290
2	2140	7260
3	4520	7260
4	5059	7260

prune841.0ms (11.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	637	0	637
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	637	2	639

Error

Counts

639 → 2

Compiler

Compiled 17642 to 7013 computations (60.2% saved)

regimes245.0ms (3.4%)

Accuracy

Total 0.0b remaining (94.3%)

Threshold costs 0.0b (94.3%)

Compiler

Compiled 2159 to 1658 computations (23.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64_1031`
2×	`sub-neg_binary64_1094`
1×	`neg-mul-1_binary64_1097` `neg-sub0_binary64_1096` `*-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` `unsub-neg_binary64_1095` `mul-1-neg_binary64_1093` `/-rgt-identity_binary64_1092` `-rgt-identity_binary64_1091` `-lft-identity_binary64_1090` `remove-double-neg_binary64_1089` `sub0-neg_binary64_1088` `--rgt-identity_binary64_1087` `+-rgt-identity_binary64_1086` `+-lft-identity_binary64_1085` `cancel-sign-sub-inv_binary64_1067` `cancel-sign-sub_binary64_1066` `distribute-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	10	20
1	13	20
2	18	20
3	20	20
4	21	20
5	21	20

end0.0ms (0%)

sample1.1s (14.5%)

Algorithm

1×

intervals

Results

285.0ms	8000×	body	128	valid
158.0ms	8000×	pre	128	true
2.0ms	121×	pre	128	false

Compiler

Compiled 286 to 216 computations (24.5% saved)

Details

analyze36.0ms (0.5%)

sample25.0ms (0.3%)

simplify174.0ms (2.4%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

rewrite64.0ms (0.9%)

series352.0ms (4.9%)

simplify81.0ms (1.1%)

prune82.0ms (1.1%)

localize8.0ms (0.1%)

rewrite589.0ms (8.1%)

series426.0ms (5.9%)

simplify464.0ms (6.4%)

prune1.9s (26.3%)

localize8.0ms (0.1%)

rewrite324.0ms (4.5%)

series319.0ms (4.4%)

simplify246.0ms (3.4%)

prune841.0ms (11.6%)

regimes245.0ms (3.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.1s (14.5%)

Profiling