Details

Time bar (total: 2.3min)

analyze296.0ms (0.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
0%0%100%2
0%0%100%3
0%0%100%4
0%0%100%5
0%0%100%6
0%0%100%7
0%0%100%8
0%0%100%9
0%0%100%10
0%0%100%11
0%0%100%12
0%0%100%13
0%0%100%14
Compiler

Compiled 30 to 24 computations (20% saved)

sample55.0ms (0%)

Algorithm
1×intervals
Results
12.0ms158×body128valid
10.0ms98×body256valid
9.0ms280×pre128true
1.0ms24×body128nan
Compiler

Compiled 50 to 47 computations (6% saved)

simplify508.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
2 → 2
Iterations

Useful iterations: 0 (401.0ms)

IterNodesCost
0183425
1183425

prune5.0ms (0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New022
Fresh022
Picked000
Done000
Total044
Error
43.0b
Counts
4 → 3
Compiler

Compiled 17 to 14 computations (17.6% saved)

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

41.9b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
0.2b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
41.9b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite42.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64_1123
14×*-un-lft-identity_binary64_1101
9×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
8×add-log-exp_binary64_1140 add-cube-cbrt_binary64_1136
6×difference-of-squares_binary64_1070 sqrt-prod_binary64_1117 associate-/l*_binary64_1046 times-frac_binary64_1107
5×pow1_binary64_1162
4×flip--_binary64_1076 flip3--_binary64_1105 cancel-sign-sub-inv_binary64_1067
3×distribute-lft-out--_binary64_1053
2×diff-log_binary64_1193 sub-neg_binary64_1094 associate-/l/_binary64_1048 sqrt-div_binary64_1118 div-exp_binary64_1152 cbrt-undiv_binary64_1135
1×rem-sqrt-square_binary64_1114 cbrt-unprod_binary64_1134 prod-exp_binary64_1150 frac-2neg_binary64_1112 sqrt-pow1_binary64_1119 clear-num_binary64_1100 div-inv_binary64_1098 associate-/r*_binary64_1045 pow1/2_binary64_1181 div-sub_binary64_1106
Counts
4 → 74
Calls

8 calls:

15.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
10.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series758.0ms (0.5%)

Counts
4 → 72
Calls

4 calls:

252.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
193.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
184.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
129.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 1950 to 1660 computations (14.9% saved)

simplify105.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
052073272

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

41.9b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.2b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
41.9b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))

rewrite46.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
19×*-un-lft-identity_binary64_1101
10×add-log-exp_binary64_1140
9×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
8×add-sqr-sqrt_binary64_1123
7×add-cube-cbrt_binary64_1136
6×distribute-lft-out_binary64_1052
5×pow1_binary64_1162 associate-/l*_binary64_1046 times-frac_binary64_1107
3×distribute-rgt-neg-in_binary64_1059 sqrt-prod_binary64_1117
2×sum-log_binary64_1192 flip--_binary64_1076 flip3--_binary64_1105 flip3-+_binary64_1104 neg-sub0_binary64_1096 associate-/l/_binary64_1048 associate-+l-_binary64_1036 sqrt-div_binary64_1118 div-exp_binary64_1152 cbrt-undiv_binary64_1135 flip-+_binary64_1075
1×diff-log_binary64_1193 rem-sqrt-square_binary64_1114 cbrt-unprod_binary64_1134 prod-exp_binary64_1150 frac-2neg_binary64_1112 sub-neg_binary64_1094 sqrt-pow1_binary64_1119 neg-log_binary64_1194 clear-num_binary64_1100 div-inv_binary64_1098 +-commutative_binary64_1031 cancel-sign-sub-inv_binary64_1067 associate-/r*_binary64_1045 pow1/2_binary64_1181 div-sub_binary64_1106
Counts
4 → 70
Calls

8 calls:

15.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
14.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series764.0ms (0.5%)

Counts
4 → 72
Calls

4 calls:

254.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
193.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
183.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
133.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 2001 to 1711 computations (14.5% saved)

simplify74.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
051673105

prune1.5s (1.1%)

Pruning

87 alts after pruning (85 fresh and 2 done)

PrunedKeptTotal
New20484288
Fresh011
Picked000
Done022
Total20487291
Error
0.1b
Counts
291 → 87
Compiler

Compiled 5601 to 3580 computations (36.1% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
0.3b
(/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

rewrite74.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
45×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
34×times-frac_binary64_1107
32×add-sqr-sqrt_binary64_1123 *-un-lft-identity_binary64_1101
17×div-exp_binary64_1152 cbrt-undiv_binary64_1135
14×associate-/l*_binary64_1046
13×cbrt-unprod_binary64_1134 prod-exp_binary64_1150
12×add-cube-cbrt_binary64_1136
10×difference-of-squares_binary64_1070 add-log-exp_binary64_1140 distribute-lft-out--_binary64_1053
8×sqrt-prod_binary64_1117 associate-/r*_binary64_1045
7×cancel-sign-sub-inv_binary64_1067
6×associate-/r/_binary64_1047
5×distribute-rgt-neg-in_binary64_1059 flip--_binary64_1076 flip3--_binary64_1105
4×pow1_binary64_1162 div-inv_binary64_1098
3×diff-log_binary64_1193
2×frac-2neg_binary64_1112 sub-neg_binary64_1094 clear-num_binary64_1100
1×neg-log_binary64_1194 neg-sub0_binary64_1096 associate-/l/_binary64_1048 associate--l-_binary64_1039
Counts
4 → 122
Calls

8 calls:

23.0ms
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
17.0ms
(/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
11.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series942.0ms (0.7%)

Counts
4 → 72
Calls

4 calls:

321.0ms
(/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
268.0ms
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
184.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
169.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
Compiler

Compiled 2487 to 2008 computations (19.3% saved)

simplify164.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 0 (107.0ms)

IterNodesCost
049475531
149475531

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
000

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (*.f64 a a) (*.f64 c c))
0.3b
(/.f64 (*.f64 a c) b)
0.1b
(/.f64 (-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b) (*.f64 a 2))
0.1b
(+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))
0.3b
(/.f64 (*.f64 a c) b)
0.3b
(*.f64 (*.f64 a a) (*.f64 c c))
0.4b
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
41.7b
(-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b)

rewrite60.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
70×add-exp-log_binary64_1139
39×add-cbrt-cube_binary64_1137
33×prod-exp_binary64_1150
32×pow1_binary64_1162
17×cbrt-unprod_binary64_1134 div-exp_binary64_1152
15×add-sqr-sqrt_binary64_1123 *-un-lft-identity_binary64_1101 times-frac_binary64_1107 associate-/r*_binary64_1045
14×pow-prod-down_binary64_1172
13×add-cube-cbrt_binary64_1136
9×add-log-exp_binary64_1140
7×cbrt-undiv_binary64_1135
6×cube-prod_binary64_1129 unpow-prod-down_binary64_1180
5×pow-exp_binary64_1169 pow-to-exp_binary64_1170
4×pow-plus_binary64_1164 pow-prod-up_binary64_1171
3×cancel-sign-sub-inv_binary64_1067
2×diff-log_binary64_1193 cube-mult_binary64_1131 frac-2neg_binary64_1112 clear-num_binary64_1100 div-inv_binary64_1098 associate-/l*_binary64_1046 unpow3_binary64_1167 pow-sqr_binary64_1074 sqr-pow_binary64_1073 pow2_binary64_1182
1×*-commutative_binary64_1032 difference-of-squares_binary64_1070 sum-log_binary64_1192 sub-neg_binary64_1094 distribute-lft-out--_binary64_1053 associate--l+_binary64_1038 flip--_binary64_1076 flip3--_binary64_1105 associate-*r*_binary64_1041 associate-*l*_binary64_1042 unswap-sqr_binary64_1069
Counts
4 → 123
Calls

8 calls:

16.0ms
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
11.0ms
(*.f64 (*.f64 a a) (*.f64 c c))
8.0ms
(-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b)
5.0ms
(/.f64 (*.f64 a c) b)
0.0ms
(+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))

series1.0s (0.7%)

Counts
4 → 42
Calls

4 calls:

541.0ms
(-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b)
263.0ms
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
125.0ms
(/.f64 (*.f64 a c) b)
86.0ms
(*.f64 (*.f64 a a) (*.f64 c c))
Compiler

Compiled 1893 to 1488 computations (21.4% saved)

simplify80.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
054462567

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b
(cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))
0.2b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)))) (*.f64 2 a))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)))
0.2b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)))) (*.f64 2 a))
0.6b
(cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))
0.7b
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)
41.9b
(+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))))

rewrite69.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
24×*-un-lft-identity_binary64_1101
12×add-sqr-sqrt_binary64_1123 add-cube-cbrt_binary64_1136 cbrt-prod_binary64_1132
10×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
8×add-log-exp_binary64_1140
6×cube-prod_binary64_1129 unpow-prod-down_binary64_1180 distribute-lft-out_binary64_1052
5×pow1_binary64_1162 associate-/l*_binary64_1046 times-frac_binary64_1107
4×cube-div_binary64_1130
3×distribute-rgt-neg-in_binary64_1059 pow-unpow_binary64_1178
2×cube-mult_binary64_1131 sum-log_binary64_1192 flip--_binary64_1076 flip3--_binary64_1105 flip3-+_binary64_1104 neg-sub0_binary64_1096 associate-/l/_binary64_1048 unpow3_binary64_1167 associate-+l-_binary64_1036 div-exp_binary64_1152 cbrt-undiv_binary64_1135 flip-+_binary64_1075 sqr-pow_binary64_1073 cbrt-div_binary64_1133
1×pow-exp_binary64_1169 rem-cube-cbrt_binary64_1124 cbrt-unprod_binary64_1134 pow1/3_binary64_1183 prod-exp_binary64_1150 pow-pow_binary64_1173 frac-2neg_binary64_1112 neg-log_binary64_1194 clear-num_binary64_1100 div-inv_binary64_1098 +-commutative_binary64_1031 pow-to-exp_binary64_1170 associate-/r*_binary64_1045 div-sub_binary64_1106 rem-cbrt-cube_binary64_1125
Counts
4 → 91
Calls

8 calls:

28.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)))) (*.f64 2 a))
18.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))))
6.0ms
(cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))
6.0ms
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)
0.0ms
(sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)))

series853.0ms (0.6%)

Counts
4 → 80
Calls

4 calls:

253.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)))) (*.f64 2 a))
232.0ms
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)
184.0ms
(cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))
183.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))))
Compiler

Compiled 2411 to 2080 computations (13.7% saved)

simplify88.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
052573989

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.1b
(sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
0.0b
(-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))
0.3b
(*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.4b
(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
0.7b
(pow.f64 (*.f64 (*.f64 4 a) c) 3)
41.7b
(-.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) b)

rewrite90.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
57×add-sqr-sqrt_binary64_1123
32×*-un-lft-identity_binary64_1101
31×times-frac_binary64_1107
27×difference-of-squares_binary64_1070
22×add-cube-cbrt_binary64_1136
21×sqr-pow_binary64_1073
17×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
15×pow1_binary64_1162
10×associate-/l*_binary64_1046
9×unpow-prod-down_binary64_1180
6×cbrt-unprod_binary64_1134 add-log-exp_binary64_1140 prod-exp_binary64_1150 pow-prod-down_binary64_1172
5×distribute-lft-out--_binary64_1053
3×pow-exp_binary64_1169 rem-cube-cbrt_binary64_1124 pow-pow_binary64_1173 pow-unpow_binary64_1178 associate-*r*_binary64_1041 cancel-sign-sub-inv_binary64_1067 associate-/r*_binary64_1045
2×flip--_binary64_1076 flip3--_binary64_1105 flip3-+_binary64_1104 sqrt-prod_binary64_1117 associate-/l/_binary64_1048 associate-*r/_binary64_1043 associate-/r/_binary64_1047 flip-+_binary64_1075
1×diff-log_binary64_1193 *-commutative_binary64_1032 cube-prod_binary64_1129 cube-mult_binary64_1131 frac-2neg_binary64_1112 sub-neg_binary64_1094 distribute-lft-in_binary64_1050 clear-num_binary64_1100 div-inv_binary64_1098 unpow3_binary64_1167 div-exp_binary64_1152 cbrt-undiv_binary64_1135 associate-*l*_binary64_1042 pow-to-exp_binary64_1170 distribute-rgt-in_binary64_1051 div-sub_binary64_1106
Counts
4 → 125
Calls

8 calls:

34.0ms
(-.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) b)
17.0ms
(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
10.0ms
(*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
6.0ms
(pow.f64 (*.f64 (*.f64 4 a) c) 3)
0.0ms
(-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))

series1.7s (1.2%)

Counts
4 → 60
Calls

4 calls:

834.0ms
(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
344.0ms
(*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
342.0ms
(-.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) b)
131.0ms
(pow.f64 (*.f64 (*.f64 4 a) c) 3)
Compiler

Compiled 2503 to 2069 computations (17.3% saved)

simplify151.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 0 (84.0ms)

IterNodesCost
052077280

prune11.8s (8.4%)

Pruning

256 alts after pruning (250 fresh and 6 done)

PrunedKeptTotal
New540175715
Fresh57580
Picked000
Done167
Total546256802
Error
0.0b
Counts
802 → 256
Compiler

Compiled 22579 to 14521 computations (35.7% saved)

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))
0.1b
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
0.1b
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
0.2b
(/.f64 (*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) a)
0.3b
(*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))

rewrite80.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
57×add-sqr-sqrt_binary64_1123 *-un-lft-identity_binary64_1101
45×times-frac_binary64_1107
36×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
29×add-cube-cbrt_binary64_1136
27×associate-*r*_binary64_1041
14×difference-of-squares_binary64_1070 distribute-lft-out--_binary64_1053
12×cbrt-unprod_binary64_1134 prod-exp_binary64_1150
10×div-exp_binary64_1152 cbrt-undiv_binary64_1135 associate-/r*_binary64_1045
9×pow1_binary64_1162
7×distribute-rgt-neg-in_binary64_1059 sqrt-prod_binary64_1117
6×add-log-exp_binary64_1140
4×associate-/l*_binary64_1046 associate-/r/_binary64_1047
3×flip--_binary64_1076 flip3--_binary64_1105 div-inv_binary64_1098 pow-prod-down_binary64_1172
2×frac-2neg_binary64_1112 clear-num_binary64_1100 associate-*r/_binary64_1043
1×diff-log_binary64_1193 *-commutative_binary64_1032 sub-neg_binary64_1094 associate-/l/_binary64_1048 associate-*l*_binary64_1042 cancel-sign-sub-inv_binary64_1067
Counts
4 → 132
Calls

8 calls:

22.0ms
(*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))
19.0ms
(/.f64 (*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) a)
12.0ms
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))

series1.0s (0.7%)

Counts
4 → 72
Calls

4 calls:

305.0ms
(*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))
268.0ms
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
267.0ms
(/.f64 (*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) a)
186.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
Compiler

Compiled 2384 to 1868 computations (21.6% saved)

simplify152.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 0 (92.0ms)

IterNodesCost
049295545
149295545

localize7.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify9.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
000

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(/.f64 (-.f64 (sqrt.f64 (log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b) (*.f64 a 2))
0.0b
(sqrt.f64 (log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.1b
(exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
11.9b
(-.f64 (sqrt.f64 (log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)
12.1b
(log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))

rewrite35.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64_1123
11×add-log-exp_binary64_1140
10×*-un-lft-identity_binary64_1101
8×add-cube-cbrt_binary64_1136
6×exp-prod_binary64_1153 cancel-sign-sub-inv_binary64_1067
5×pow1_binary64_1162 log-prod_binary64_1187
4×exp-sum_binary64_1147 add-exp-log_binary64_1139 sub-neg_binary64_1094 add-cbrt-cube_binary64_1137 log-pow_binary64_1190
3×diff-log_binary64_1193
2×difference-of-squares_binary64_1070 rem-exp-log_binary64_1141 exp-diff_binary64_1149 flip--_binary64_1076 flip3--_binary64_1105
1×rem-log-exp_binary64_1142 distribute-lft-out--_binary64_1053 sqrt-prod_binary64_1117 log-div_binary64_1188
Counts
4 → 62
Calls

8 calls:

11.0ms
(-.f64 (sqrt.f64 (log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)
7.0ms
(log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
6.0ms
(exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(sqrt.f64 (log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

series1.3s (0.9%)

Counts
4 → 66
Calls

4 calls:

504.0ms
(log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
457.0ms
(-.f64 (sqrt.f64 (log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)
192.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
132.0ms
(exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 2016 to 1786 computations (11.4% saved)

simplify122.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (93.0ms)

IterNodesCost
049402313
149402313

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2))))) (*.f64 2 a))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2))))
0.4b
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)
0.5b
(*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2))
0.6b
(cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)))
41.9b
(+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)))))

rewrite64.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
26×add-sqr-sqrt_binary64_1123
21×unpow-prod-down_binary64_1180
18×*-un-lft-identity_binary64_1101
17×add-exp-log_binary64_1139
14×add-cube-cbrt_binary64_1136
11×sqr-pow_binary64_1073
9×prod-exp_binary64_1150 unswap-sqr_binary64_1069
8×add-log-exp_binary64_1140
7×pow-exp_binary64_1169 swap-sqr_binary64_1068 associate-*r*_binary64_1041 associate-*l*_binary64_1042 pow-to-exp_binary64_1170
6×add-cbrt-cube_binary64_1137
5×pow1_binary64_1162
3×pow-unpow_binary64_1178
2×distribute-lft-out_binary64_1052 sum-log_binary64_1192
1×distribute-rgt-neg-in_binary64_1059 *-commutative_binary64_1032 cbrt-unprod_binary64_1134 pow1/3_binary64_1183 pow-prod-up_binary64_1171 pow-pow_binary64_1173 neg-log_binary64_1194 flip3-+_binary64_1104 neg-sub0_binary64_1096 pow-sqr_binary64_1074 associate-+l-_binary64_1036 +-commutative_binary64_1031 pow-prod-down_binary64_1172 flip-+_binary64_1075 pow2_binary64_1182 cbrt-prod_binary64_1132
Counts
4 → 93
Calls

8 calls:

16.0ms
(*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2))
14.0ms
(cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)))
11.0ms
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)
9.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)))))
0.0ms
(sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2))))

series931.0ms (0.7%)

Counts
4 → 81
Calls

4 calls:

261.0ms
(*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2))
261.0ms
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)
207.0ms
(cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)))
203.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)))))
Compiler

Compiled 2935 to 2478 computations (15.6% saved)

simplify124.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
050644109

localize34.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(+.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.1b
(*.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)))
0.3b
(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))) 3)) (*.f64 (+.f64 (*.f64 b b) (+.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))) (*.f64 a 2)))
0.6b
(cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))
0.7b
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)
41.2b
(+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))) 3))

rewrite187.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
66×*-un-lft-identity_binary64_1101
30×cube-prod_binary64_1129 unpow-prod-down_binary64_1180
27×distribute-lft-out_binary64_1052
14×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
13×associate-/l*_binary64_1046 times-frac_binary64_1107
12×distribute-rgt-neg-in_binary64_1059 add-sqr-sqrt_binary64_1123 add-cube-cbrt_binary64_1136 cbrt-prod_binary64_1132
6×add-log-exp_binary64_1140
5×pow1_binary64_1162
4×cube-div_binary64_1130
3×cbrt-unprod_binary64_1134 prod-exp_binary64_1150 flip3-+_binary64_1104 pow-unpow_binary64_1178 sum-cubes_binary64_1102 div-exp_binary64_1152 cbrt-undiv_binary64_1135 flip-+_binary64_1075
2×cube-mult_binary64_1131 flip--_binary64_1076 flip3--_binary64_1105 associate-/l/_binary64_1048 associate-/r/_binary64_1047 unpow3_binary64_1167 associate-*l/_binary64_1044 sqr-pow_binary64_1073 cbrt-div_binary64_1133
1×pow-exp_binary64_1169 rem-cube-cbrt_binary64_1124 pow1/3_binary64_1183 pow-pow_binary64_1173 frac-2neg_binary64_1112 sum-log_binary64_1192 clear-num_binary64_1100 div-inv_binary64_1098 +-commutative_binary64_1031 pow-to-exp_binary64_1170 associate-/r*_binary64_1045 rem-cbrt-cube_binary64_1125
Counts
4 → 116
Calls

8 calls:

82.0ms
(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))) 3)) (*.f64 (+.f64 (*.f64 b b) (+.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))) (*.f64 a 2)))
69.0ms
(+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))) 3))
7.0ms
(cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))
6.0ms
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)
0.0ms
(sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)))

series1.4s (1%)

Counts
4 → 81
Calls

4 calls:

532.0ms
(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))) 3)) (*.f64 (+.f64 (*.f64 b b) (+.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))) (*.f64 a 2)))
322.0ms
(+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))) 3))
278.0ms
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)
227.0ms
(cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))
Compiler

Compiled 5081 to 3639 computations (28.4% saved)

simplify125.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
055286850

prune16.4s (11.7%)

Pruning

429 alts after pruning (419 fresh and 10 done)

PrunedKeptTotal
New509194703
Fresh20225245
Picked000
Done11011
Total530429959
Error
0b
Counts
959 → 429
Compiler

Compiled 29912 to 19376 computations (35.2% saved)

localize32.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (+.f64 (pow.f64 b 4) (*.f64 -16 (*.f64 (*.f64 c c) (*.f64 a a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
0.1b
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (+.f64 (pow.f64 b 4) (*.f64 -16 (*.f64 (*.f64 c c) (*.f64 a a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
0.1b
(sqrt.f64 (/.f64 (+.f64 (pow.f64 b 4) (*.f64 -16 (*.f64 (*.f64 c c) (*.f64 a a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
0.1b
(+.f64 (pow.f64 b 4) (*.f64 -16 (*.f64 (*.f64 c c) (*.f64 a a))))
0.2b
(/.f64 (*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (+.f64 (pow.f64 b 4) (*.f64 -16 (*.f64 (*.f64 c c) (*.f64 a a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))) a)
0.3b
(*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (+.f64 (pow.f64 b 4) (*.f64 -16 (*.f64 (*.f64 c c) (*.f64 a a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))
0.3b
(*.f64 (*.f64 c c) (*.f64 a a))
0.4b
(/.f64 (+.f64 (pow.f64 b 4) (*.f64 -16 (*.f64 (*.f64 c c) (*.f64 a a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))

rewrite117.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
48×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
47×add-sqr-sqrt_binary64_1123
39×times-frac_binary64_1107
38×*-un-lft-identity_binary64_1101
37×pow1_binary64_1162
31×associate-*r*_binary64_1041
26×add-cube-cbrt_binary64_1136
20×cbrt-unprod_binary64_1134 prod-exp_binary64_1150
17×pow-prod-down_binary64_1172
10×div-exp_binary64_1152 cbrt-undiv_binary64_1135
9×difference-of-squares_binary64_1070
6×distribute-lft-out--_binary64_1053 sqrt-prod_binary64_1117 associate-/r*_binary64_1045
4×pow-plus_binary64_1164 pow-prod-up_binary64_1171 add-log-exp_binary64_1140 associate-/l*_binary64_1046 associate-/r/_binary64_1047
3×distribute-rgt-neg-in_binary64_1059 associate-/l/_binary64_1048 div-inv_binary64_1098
2×*-commutative_binary64_1032 frac-2neg_binary64_1112 clear-num_binary64_1100 flip3-+_binary64_1104 associate-*r/_binary64_1043 pow-sqr_binary64_1074 flip-+_binary64_1075 associate-*l*_binary64_1042 pow2_binary64_1182
1×flip--_binary64_1076 flip3--_binary64_1105 unswap-sqr_binary64_1069
Counts
4 → 138
Calls

8 calls:

39.0ms
(/.f64 (*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (+.f64 (pow.f64 b 4) (*.f64 -16 (*.f64 (*.f64 c c) (*.f64 a a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))) a)
32.0ms
(*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (+.f64 (pow.f64 b 4) (*.f64 -16 (*.f64 (*.f64 c c) (*.f64 a a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))
13.0ms
(/.f64 (+.f64 (pow.f64 b 4) (*.f64 -16 (*.f64 (*.f64 c c) (*.f64 a a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
10.0ms
(*.f64 (*.f64 c c) (*.f64 a a))
0.0ms
(+.f64 (pow.f64 b 4) (*.f64 -16 (*.f64 (*.f64 c c) (*.f64 a a))))

series1.3s (0.9%)

Counts
4 → 60
Calls

4 calls:

491.0ms
(/.f64 (+.f64 (pow.f64 b 4) (*.f64 -16 (*.f64 (*.f64 c c) (*.f64 a a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
393.0ms
(*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (+.f64 (pow.f64 b 4) (*.f64 -16 (*.f64 (*.f64 c c) (*.f64 a a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))
328.0ms
(/.f64 (*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (+.f64 (pow.f64 b 4) (*.f64 -16 (*.f64 (*.f64 c c) (*.f64 a a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))) a)
87.0ms
(*.f64 (*.f64 c c) (*.f64 a a))
Compiler

Compiled 2117 to 1662 computations (21.5% saved)

simplify179.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 0 (113.0ms)

IterNodesCost
049426681
149426681

localize5.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
000

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 c (+.f64 (/.f64 a b) (*.f64 (/.f64 (*.f64 a a) (pow.f64 b 3)) c)))
0.2b
(*.f64 (/.f64 (*.f64 a a) (pow.f64 b 3)) c)
0.2b
(/.f64 (cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 c (+.f64 (/.f64 a b) (*.f64 (/.f64 (*.f64 a a) (pow.f64 b 3)) c)))) 3)) (*.f64 a 2))
0.1b
(+.f64 (/.f64 a b) (*.f64 (/.f64 (*.f64 a a) (pow.f64 b 3)) c))
0.3b
(*.f64 c (+.f64 (/.f64 a b) (*.f64 (/.f64 (*.f64 a a) (pow.f64 b 3)) c)))
0.4b
(/.f64 (*.f64 a a) (pow.f64 b 3))
0.6b
(cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 c (+.f64 (/.f64 a b) (*.f64 (/.f64 (*.f64 a a) (pow.f64 b 3)) c)))) 3))
0.7b
(pow.f64 (*.f64 -2 (*.f64 c (+.f64 (/.f64 a b) (*.f64 (/.f64 (*.f64 a a) (pow.f64 b 3)) c)))) 3)

rewrite51.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
25×add-exp-log_binary64_1139
17×add-cbrt-cube_binary64_1137
16×add-sqr-sqrt_binary64_1123
15×associate-*r/_binary64_1043
14×*-un-lft-identity_binary64_1101 add-cube-cbrt_binary64_1136
12×pow1_binary64_1162 times-frac_binary64_1107 associate-/r*_binary64_1045
8×cube-prod_binary64_1129 unpow-prod-down_binary64_1180 cbrt-prod_binary64_1132
7×prod-exp_binary64_1150
6×cube-div_binary64_1130 div-exp_binary64_1152
5×pow-exp_binary64_1169 cbrt-unprod_binary64_1134
4×cube-mult_binary64_1131 add-log-exp_binary64_1140 unpow3_binary64_1167 pow-prod-down_binary64_1172 sqr-pow_binary64_1073
3×rem-cube-cbrt_binary64_1124 pow-pow_binary64_1173 flip3-+_binary64_1104 pow-unpow_binary64_1178 associate-*r*_binary64_1041 flip-+_binary64_1075 associate-*l*_binary64_1042 frac-add_binary64_1109 associate-*l/_binary64_1044 pow-to-exp_binary64_1170 cbrt-div_binary64_1133
2×cbrt-undiv_binary64_1135
1×*-commutative_binary64_1032 pow1/3_binary64_1183 frac-2neg_binary64_1112 distribute-lft-in_binary64_1050 clear-num_binary64_1100 div-inv_binary64_1098 associate-/l*_binary64_1046 unswap-sqr_binary64_1069 distribute-rgt-in_binary64_1051 rem-cbrt-cube_binary64_1125
Counts
4 → 114
Calls

8 calls:

14.0ms
(pow.f64 (*.f64 -2 (*.f64 c (+.f64 (/.f64 a b) (*.f64 (/.f64 (*.f64 a a) (pow.f64 b 3)) c)))) 3)
12.0ms
(*.f64 c (+.f64 (/.f64 a b) (*.f64 (/.f64 (*.f64 a a) (pow.f64 b 3)) c)))
7.0ms
(/.f64 (*.f64 a a) (pow.f64 b 3))
4.0ms
(cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 c (+.f64 (/.f64 a b) (*.f64 (/.f64 (*.f64 a a) (pow.f64 b 3)) c)))) 3))
0.0ms
(+.f64 (/.f64 a b) (*.f64 (/.f64 (*.f64 a a) (pow.f64 b 3)) c))

series1.3s (1%)

Counts
4 → 55
Calls

4 calls:

534.0ms
(cbrt.f64 (pow.f64 (*.f64 -2 (*.f64 c (+.f64 (/.f64 a b) (*.f64 (/.f64 (*.f64 a a) (pow.f64 b 3)) c)))) 3))
450.0ms
(*.f64 c (+.f64 (/.f64 a b) (*.f64 (/.f64 (*.f64 a a) (pow.f64 b 3)) c)))
238.0ms
(pow.f64 (*.f64 -2 (*.f64 c (+.f64 (/.f64 a b) (*.f64 (/.f64 (*.f64 a a) (pow.f64 b 3)) c)))) 3)
118.0ms
(/.f64 (*.f64 a a) (pow.f64 b 3))
Compiler

Compiled 2177 to 1894 computations (13% saved)

simplify105.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
049733692
149733692

localize20.0ms (0%)

Local error

Found 6 expressions with local error:

30.4b
(log.f64 (pow.f64 (pow.f64 (exp.f64 c) a) -4))
8.1b
(pow.f64 (exp.f64 c) a)
0.8b
(pow.f64 (pow.f64 (exp.f64 c) a) -4)
0.8b
(pow.f64 (pow.f64 (exp.f64 c) a) -4)
8.1b
(pow.f64 (exp.f64 c) a)
30.4b
(log.f64 (pow.f64 (pow.f64 (exp.f64 c) a) -4))

rewrite19.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
23×unpow-prod-down_binary64_1180
12×add-sqr-sqrt_binary64_1123 *-un-lft-identity_binary64_1101 add-cube-cbrt_binary64_1136
11×log-prod_binary64_1187
9×pow-exp_binary64_1169
6×add-exp-log_binary64_1139 pow-unpow_binary64_1178
5×pow-pow_binary64_1173 rem-log-exp_binary64_1142 sqr-pow_binary64_1073 pow-to-exp_binary64_1170
4×pow1_binary64_1162
3×add-log-exp_binary64_1140 exp-prod_binary64_1153 add-cbrt-cube_binary64_1137
1×log-pow_binary64_1190
Counts
3 → 67
Calls

6 calls:

5.0ms
(log.f64 (pow.f64 (pow.f64 (exp.f64 c) a) -4))
5.0ms
(pow.f64 (pow.f64 (exp.f64 c) a) -4)
4.0ms
(pow.f64 (exp.f64 c) a)
0.0ms
(pow.f64 (pow.f64 (exp.f64 c) a) -4)
0.0ms
(pow.f64 (exp.f64 c) a)

series933.0ms (0.7%)

Counts
3 → 18
Calls

3 calls:

657.0ms
(log.f64 (pow.f64 (pow.f64 (exp.f64 c) a) -4))
202.0ms
(pow.f64 (pow.f64 (exp.f64 c) a) -4)
73.0ms
(pow.f64 (exp.f64 c) a)
Compiler

Compiled 524 to 496 computations (5.3% saved)

simplify111.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 0 (92.0ms)

IterNodesCost
05098854

localize34.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.4b
(-.f64 (pow.f64 b 4) (*.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (+.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))))
0.4b
(*.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (+.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)))
0.4b
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)
41.2b
(-.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 b 3))

rewrite96.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64_1123 frac-times_binary64_1111
18×flip3-+_binary64_1104 flip-+_binary64_1075
14×associate-*r/_binary64_1043
13×unpow-prod-down_binary64_1180 cancel-sign-sub-inv_binary64_1067
12×difference-of-squares_binary64_1070 *-un-lft-identity_binary64_1101
11×flip--_binary64_1076 flip3--_binary64_1105
10×add-exp-log_binary64_1139 pow1_binary64_1162 add-cube-cbrt_binary64_1136
9×add-cbrt-cube_binary64_1137 sqr-pow_binary64_1073
8×add-log-exp_binary64_1140 distribute-lft-in_binary64_1050 associate-*l/_binary64_1044 distribute-rgt-in_binary64_1051
6×cube-prod_binary64_1129
4×associate--r+_binary64_1037
3×cbrt-unprod_binary64_1134 prod-exp_binary64_1150 pow-unpow_binary64_1178 pow-prod-down_binary64_1172 associate-*l*_binary64_1042
2×diff-log_binary64_1193 sub-neg_binary64_1094
1×*-commutative_binary64_1032 pow-exp_binary64_1169 cube-mult_binary64_1131 pow-pow_binary64_1173 distribute-lft-out--_binary64_1053 unpow3_binary64_1167 associate-*r*_binary64_1041 unswap-sqr_binary64_1069 pow-to-exp_binary64_1170
Counts
4 → 118
Calls

8 calls:

35.0ms
(*.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (+.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)))
14.0ms
(-.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 b 3))
7.0ms
(-.f64 (pow.f64 b 4) (*.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (+.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))))
5.0ms
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series1.4s (1%)

Counts
4 → 70
Calls

4 calls:

480.0ms
(-.f64 (pow.f64 b 4) (*.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (+.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))))
374.0ms
(*.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (+.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)))
298.0ms
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)
251.0ms
(-.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 b 3))
Compiler

Compiled 7926 to 5175 computations (34.7% saved)

simplify186.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 0 (110.0ms)

IterNodesCost
050207932

prune30.9s (22%)

Pruning

633 alts after pruning (619 fresh and 14 done)

PrunedKeptTotal
New413227640
Fresh22392414
Picked000
Done11415
Total4366331069
Error
0b
Counts
1069 → 633
Compiler

Compiled 19431 to 10530 computations (45.8% saved)

simplify943.0ms (0.7%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
0533665440

regimes15.3s (10.9%)

Compiler

Compiled 161733 to 110296 computations (31.8% saved)

bsearch0.0ms (0%)

regimes5.2s (3.7%)

Compiler

Compiled 42145 to 31616 computations (25% saved)

bsearch0.0ms (0%)

regimes554.0ms (0.4%)

Compiler

Compiled 4581 to 3812 computations (16.8% saved)

bsearch0.0ms (0%)

regimes490.0ms (0.3%)

Compiler

Compiled 4097 to 3444 computations (15.9% saved)

bsearch0.0ms (0%)

regimes179.0ms (0.1%)

Compiler

Compiled 1209 to 1044 computations (13.6% saved)

bsearch0.0ms (0%)

regimes98.0ms (0.1%)

Compiler

Compiled 510 to 516 computations (-1.2% saved)

bsearch0.0ms (0%)

regimes28.0ms (0%)

Accuracy

Total 0.3b remaining (100%)

Threshold costs 0.3b (100%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch8.0ms (0%)

Compiler

Compiled 113 to 94 computations (16.8% saved)

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0236167
1236167

end0.0ms (0%)

sample37.4s (26.6%)

Algorithm
1×intervals
Results
299.0ms2920×body256valid
285.0ms8946×pre128true
262.0ms5079×body128valid
48.0ms946×body128nan
0.0ms1×body512valid
Compiler

Compiled 40657 to 27756 computations (31.7% saved)

Pareto

0.9368646928667187

Profiling

Loading profile data...