Details

analyze5.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Compiler

Compiled 42 to 29 computations (31% saved)

sample31.0ms (0.1%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify313.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

912×	`unswap-sqr_binary64_1069`
690×	`distribute-rgt-in_binary64_1051`
658×	`distribute-lft-in_binary64_1050`
542×	`associate-/l/_binary64_1048`
492×	`associate-l_binary64_1042`
387×	`*-commutative_binary64_1032`
382×	`associate-+r+_binary64_1033`
377×	`associate-+l+_binary64_1034`
357×	`associate-/l*_binary64_1046`
343×	`+-commutative_binary64_1031`
330×	`times-frac_binary64_1107`
320×	`associate-/r/_binary64_1047`
283×	`associate-*l/_binary64_1044`
253×	`associate-/r*_binary64_1045`
241×	`associate-r_binary64_1041`
161×	`sqr-pow_binary64_1073`
143×	`distribute-rgt-out_binary64_1054`
137×	`pow-sqr_binary64_1074`
69×	`*-lft-identity_binary64_1090`
65×	`/-rgt-identity_binary64_1092`
47×	`associate-*r/_binary64_1043`
44×	`*-rgt-identity_binary64_1091`
36×	`remove-double-div_binary64_1077`
23×	`distribute-lft-out_binary64_1052`
19×	`distribute-rgt1-in_binary64_1057`
12×	`swap-sqr_binary64_1068`
9×	`pow-base-1_binary64_1161`
6×	`cube-prod_binary64_1129`
5×	`distribute-lft1-in_binary64_1056`
4×	`cube-div_binary64_1130`
2×	`unpow3_binary64_1167` `cube-unmult_binary64_1138`
1×	`1-exp_binary64_1145` `cube-mult_binary64_1131`
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` `unpow2_binary64_1166` `unpow1/2_binary64_1165` `pow-plus_binary64_1164` `exp-to-pow_binary64_1163` `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` `cube-neg_binary64_1128` `rem-3cbrt-rft_binary64_1127` `rem-3cbrt-lft_binary64_1126` `rem-cbrt-cube_binary64_1125` `rem-cube-cbrt_binary64_1124` `sqr-abs_binary64_1116` `sqr-neg_binary64_1115` `rem-sqrt-square_binary64_1114` `rem-square-sqrt_binary64_1113` `div-sub_binary64_1106` `neg-mul-1_binary64_1097` `neg-sub0_binary64_1096` `unsub-neg_binary64_1095` `sub-neg_binary64_1094` `mul-1-neg_binary64_1093` `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-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-rgt-out--_binary64_1055` `distribute-lft-out--_binary64_1053` `count-2_binary64_1049` `associate--r-_binary64_1040` `associate--l-_binary64_1039` `associate--l+_binary64_1038` `associate--r+_binary64_1037` `associate-+l-_binary64_1036` `associate-+r-_binary64_1035`

Counts

1 → 7

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	36	43
2	110	43
3	440	40
4	2140	40
5	2159	40
6	2249	40
7	2496	40
8	2857	40
9	2839	40
10	2972	40
11	3198	40
12	3491	40
13	3589	40
14	4252	40
15	4178	40

prune18.0ms (0.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	4	3	7
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	4	4	8

Error

1.5b

Counts

8 → 4

Compiler

Compiled 313 to 206 computations (34.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2)))
0.0b	(*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 2 (+.f64 (+.f64 alpha beta) 1)))
0.1b	(.f64 (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2))) (/.f64 (+.f64 alpha 1) (.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 2 (+.f64 (+.f64 alpha beta) 1)))))
13.1b	(/.f64 (+.f64 alpha 1) (*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 2 (+.f64 (+.f64 alpha beta) 1))))

rewrite701.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

118×	`*-un-lft-identity_binary64_1101`
50×	`distribute-lft-out_binary64_1052`
49×	`times-frac_binary64_1107`
38×	`add-sqr-sqrt_binary64_1123`
34×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
31×	`add-cube-cbrt_binary64_1136` `associate-l_binary64_1042`
22×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-r_binary64_1041`
20×	`associate-/r/_binary64_1047`
13×	`frac-times_binary64_1111`
10×	`prod-exp_binary64_1150` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cbrt-unprod_binary64_1134`
8×	`pow1_binary64_1162` `associate-/l*_binary64_1046`
7×	`associate-l/_binary64_1044` `associate-r/_binary64_1043`
6×	`associate-/r*_binary64_1045`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098` `associate-/l/_binary64_1048`
3×	`unswap-sqr_binary64_1069`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `pow-prod-down_binary64_1172` `*-commutative_binary64_1032`
1×	`distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`

Counts

4 → 179

Calls

4 calls:

36.0ms	(.f64 (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2))) (/.f64 (+.f64 alpha 1) (.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 2 (+.f64 (+.f64 alpha beta) 1)))))
18.0ms	(/.f64 (+.f64 alpha 1) (*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 2 (+.f64 (+.f64 alpha beta) 1))))
16.0ms	(*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 2 (+.f64 (+.f64 alpha beta) 1)))
13.0ms	(/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2)))

Compiler

Compiled 7398 to 5083 computations (31.3% saved)

series2.1s (10.2%)

Error

1.1b

Counts

4 → 69

Calls

4 calls:

1.1s	(.f64 (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2))) (/.f64 (+.f64 alpha 1) (.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 2 (+.f64 (+.f64 alpha beta) 1)))))
412.0ms	(/.f64 (+.f64 alpha 1) (*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 2 (+.f64 (+.f64 alpha beta) 1))))
169.0ms	(/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2)))
152.0ms	(*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 2 (+.f64 (+.f64 alpha beta) 1)))

Compiler

Compiled 13095 to 10294 computations (21.4% saved)

simplify1.2s (5.6%)

Algorithm

1×	egg-herbie

Rules

441×	`distribute-rgt-in_binary64_1051`
417×	`distribute-lft-in_binary64_1050`
235×	`+-commutative_binary64_1031`
224×	`*-commutative_binary64_1032`
170×	`associate-+r+_binary64_1033`
135×	`associate-*r/_binary64_1043`
128×	`sub-neg_binary64_1094`
124×	`associate-/r*_binary64_1045`
81×	`distribute-neg-in_binary64_1062`
80×	`associate-/l*_binary64_1046`
79×	`unswap-sqr_binary64_1069`
74×	`times-frac_binary64_1107`
63×	`sqr-pow_binary64_1073` `cancel-sign-sub-inv_binary64_1067`
38×	`neg-mul-1_binary64_1097` `neg-sub0_binary64_1096`
31×	`associate-*l/_binary64_1044`
27×	`associate--r+_binary64_1037`
23×	`associate-r_binary64_1041` `associate--l+_binary64_1038`
21×	`pow-sqr_binary64_1074`
18×	`swap-sqr_binary64_1068`
17×	`*-rgt-identity_binary64_1091`
16×	`associate-l_binary64_1042`
15×	`distribute-rgt-neg-in_binary64_1059`
10×	`distribute-rgt-out_binary64_1054`
9×	`distribute-lft-neg-in_binary64_1058`
8×	`unpow2_binary64_1166` `exp-prod_binary64_1153` `cube-unmult_binary64_1138`
7×	`log-div_binary64_1188` `unpow3_binary64_1167` `cube-mult_binary64_1131` `*-lft-identity_binary64_1090` `associate-+r-_binary64_1035`
6×	`log-prod_binary64_1187`
5×	`pow-plus_binary64_1164` `difference-of-squares_binary64_1070` `distribute-rgt-out--_binary64_1055`
4×	`exp-sum_binary64_1147` `cube-prod_binary64_1129` `/-rgt-identity_binary64_1092` `distribute-lft-neg-out_binary64_1060`
3×	`unsub-neg_binary64_1095` `associate-+l-_binary64_1036`
2×	`distribute-neg-frac_binary64_1065` `distribute-rgt1-in_binary64_1057` `distribute-lft-out_binary64_1052`
1×	`1-exp_binary64_1145` `*-inverses_binary64_1081` `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` `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` `div-exp_binary64_1152` `rec-exp_binary64_1151` `prod-exp_binary64_1150` `exp-diff_binary64_1149` `exp-neg_binary64_1148` `e-exp-1_binary64_1146` `exp-1-e_binary64_1144` `exp-0_binary64_1143` `rem-log-exp_binary64_1142` `rem-exp-log_binary64_1141` `cube-div_binary64_1130` `cube-neg_binary64_1128` `rem-3cbrt-rft_binary64_1127` `rem-3cbrt-lft_binary64_1126` `rem-cbrt-cube_binary64_1125` `rem-cube-cbrt_binary64_1124` `sqr-abs_binary64_1116` `sqr-neg_binary64_1115` `rem-sqrt-square_binary64_1114` `rem-square-sqrt_binary64_1113` `div-sub_binary64_1106` `mul-1-neg_binary64_1093` `remove-double-neg_binary64_1089` `sub0-neg_binary64_1088` `--rgt-identity_binary64_1087` `+-rgt-identity_binary64_1086` `+-lft-identity_binary64_1085` `mul0-rgt_binary64_1084` `mul0-lft_binary64_1083` `div0_binary64_1082` `+-inverses_binary64_1080` `lft-mult-inverse_binary64_1079` `rgt-mult-inverse_binary64_1078` `remove-double-div_binary64_1077` `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-lft1-in_binary64_1056` `distribute-lft-out--_binary64_1053` `count-2_binary64_1049` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `associate--r-_binary64_1040` `associate--l-_binary64_1039`

Counts

248 → 402

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	831	13926
1	2845	12711

prune1.8s (8.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	398	4	402
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	399	7	406

Error

Counts

406 → 7

Compiler

Compiled 23139 to 16146 computations (30.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 1 (+.f64 beta alpha))))
0.0b	(/.f64 (+.f64 (+.f64 2 beta) alpha) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 1 (+.f64 beta alpha)))))
0.1b	(/.f64 1 (/.f64 (+.f64 (+.f64 2 beta) alpha) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 1 (+.f64 beta alpha))))))
0.1b	(*.f64 (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2))) (/.f64 1 (/.f64 (+.f64 (+.f64 2 beta) alpha) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 1 (+.f64 beta alpha)))))))

rewrite11.0s (52.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

4305×	`*-un-lft-identity_binary64_1101`
3189×	`times-frac_binary64_1107`
2007×	`distribute-lft-out_binary64_1052`
1090×	`add-sqr-sqrt_binary64_1123`
1037×	`add-cube-cbrt_binary64_1136`
470×	`associate-r_binary64_1041`
191×	`associate-/r*_binary64_1045`
106×	`add-exp-log_binary64_1139`
96×	`associate-/r/_binary64_1047`
59×	`div-exp_binary64_1152`
53×	`div-inv_binary64_1098`
52×	`add-cbrt-cube_binary64_1137`
45×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
26×	`cbrt-undiv_binary64_1135` `associate-l_binary64_1042`
20×	`prod-exp_binary64_1150`
14×	`unswap-sqr_binary64_1069`
12×	`associate-/l*_binary64_1046`
9×	`1-exp_binary64_1145` `rec-exp_binary64_1151`
8×	`cbrt-unprod_binary64_1134`
7×	`pow1_binary64_1162`
4×	`add-log-exp_binary64_1140` `associate-/l/_binary64_1048`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100`
1×	`pow-prod-down_binary64_1172` `frac-times_binary64_1111` `un-div-inv_binary64_1099` `associate-l/_binary64_1044` `associate-r/_binary64_1043` `*-commutative_binary64_1032` `inv-pow_binary64_1186` `pow-flip_binary64_1175`

Counts

4 → 1451

Calls

4 calls:

268.0ms	(*.f64 (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2))) (/.f64 1 (/.f64 (+.f64 (+.f64 2 beta) alpha) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 1 (+.f64 beta alpha)))))))
49.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 2 beta) alpha) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 1 (+.f64 beta alpha))))))
23.0ms	(/.f64 (+.f64 (+.f64 2 beta) alpha) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 1 (+.f64 beta alpha)))))
12.0ms	(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 1 (+.f64 beta alpha))))

Compiler

Compiled 71068 to 52479 computations (26.2% saved)

series2.1s (10.2%)

Error

Counts

4 → 67

Calls

4 calls:

1.0s	(*.f64 (/.f64 (+.f64 beta 1) (+.f64 alpha (+.f64 beta 2))) (/.f64 1 (/.f64 (+.f64 (+.f64 2 beta) alpha) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 1 (+.f64 beta alpha)))))))
429.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 2 beta) alpha) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 1 (+.f64 beta alpha))))))
213.0ms	(/.f64 (+.f64 (+.f64 2 beta) alpha) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 1 (+.f64 beta alpha)))))
146.0ms	(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 1 (+.f64 beta alpha))))

Compiler

Compiled 13049 to 10299 computations (21.1% saved)

simplify1.5s (7.3%)

Algorithm

1×	egg-herbie

Rules

348×	`*-commutative_binary64_1032`
336×	`associate-/r/_binary64_1047`
288×	`associate-*r/_binary64_1043`
234×	`+-commutative_binary64_1031`
179×	`associate-*l/_binary64_1044`
171×	`associate-+r+_binary64_1033`
145×	`associate-/l*_binary64_1046`
142×	`sub-neg_binary64_1094`
121×	`associate-/r*_binary64_1045`
83×	`unswap-sqr_binary64_1069`
81×	`distribute-neg-in_binary64_1062`
74×	`times-frac_binary64_1107` `cancel-sign-sub-inv_binary64_1067`
60×	`sqr-pow_binary64_1073`
41×	`neg-mul-1_binary64_1097`
40×	`neg-sub0_binary64_1096`
33×	`*-rgt-identity_binary64_1091`
27×	`associate--r+_binary64_1037`
25×	`associate--l+_binary64_1038`
23×	`distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`
20×	`pow-sqr_binary64_1074` `associate-r_binary64_1041`
18×	`remove-double-div_binary64_1077`
16×	`swap-sqr_binary64_1068`
15×	`/-rgt-identity_binary64_1092` `associate-l_binary64_1042`
12×	`associate-+r-_binary64_1035`
11×	`log-div_binary64_1188`
10×	`log-prod_binary64_1187` `cube-unmult_binary64_1138`
9×	`unsub-neg_binary64_1095` `distribute-neg-frac_binary64_1065` `associate-+l-_binary64_1036`
8×	`unpow2_binary64_1166`
7×	`exp-prod_binary64_1153` `*-lft-identity_binary64_1090`
6×	`unpow3_binary64_1167` `cube-mult_binary64_1131` `associate-/l/_binary64_1048`
5×	`pow-plus_binary64_1164`
4×	`distribute-rgt-out--_binary64_1055` `associate--r-_binary64_1040`
3×	`log-rec_binary64_1189`
2×	`cube-prod_binary64_1129` `div-sub_binary64_1106` `distribute-lft-out_binary64_1052`
1×	`1-exp_binary64_1145` `sub0-neg_binary64_1088` `+-rgt-identity_binary64_1086` `*-inverses_binary64_1081` `difference-of-squares_binary64_1070` `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` `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` `div-exp_binary64_1152` `rec-exp_binary64_1151` `prod-exp_binary64_1150` `exp-diff_binary64_1149` `exp-neg_binary64_1148` `exp-sum_binary64_1147` `e-exp-1_binary64_1146` `exp-1-e_binary64_1144` `exp-0_binary64_1143` `rem-log-exp_binary64_1142` `rem-exp-log_binary64_1141` `cube-div_binary64_1130` `cube-neg_binary64_1128` `rem-3cbrt-rft_binary64_1127` `rem-3cbrt-lft_binary64_1126` `rem-cbrt-cube_binary64_1125` `rem-cube-cbrt_binary64_1124` `sqr-abs_binary64_1116` `sqr-neg_binary64_1115` `rem-sqrt-square_binary64_1114` `rem-square-sqrt_binary64_1113` `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` `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-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_1054` `distribute-lft-out--_binary64_1053` `count-2_binary64_1049` `associate--l-_binary64_1039`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1388	70817
1	4315	69297

Details

analyze5.0ms (0%)

sample31.0ms (0.1%)

simplify313.0ms (1.5%)

prune18.0ms (0.1%)

localize16.0ms (0.1%)

rewrite701.0ms (3.4%)

series2.1s (10.2%)

simplify1.2s (5.6%)

prune1.8s (8.8%)

localize16.0ms (0.1%)

rewrite11.0s (52.7%)

series2.1s (10.2%)

simplify1.5s (7.3%)

end0.0ms (0%)

Profiling