Details

Time bar (total: 2.4min)

analyze262.0ms (0.2%)

Algorithm
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)

sample46.0ms (0%)

Algorithm
intervals
Results
14.0ms119×body256valid
9.0ms280×pre128true
7.0ms52×body512valid
4.0ms85×body128valid
1.0ms24×body128nan
Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify427.0ms (0.3%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (332.0ms)

IterNodesCost
0183424
1183424

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
52.8b
Counts
2 → 2
Compiler

Compiled 16 to 13 computations (18.8% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

25.2b
(+.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))
0.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(/.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))
25.2b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))

rewrite43.0ms (0%)

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity_binary64_1101
10×add-log-exp_binary64_1140
add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
add-sqr-sqrt_binary64_1123
add-cube-cbrt_binary64_1136
distribute-lft-out_binary64_1052
pow1_binary64_1162 associate-/l*_binary64_1046 times-frac_binary64_1107
distribute-rgt-neg-in_binary64_1059 sqrt-prod_binary64_1117
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
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:

17.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
10.0ms
(+.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))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series646.0ms (0.5%)

Counts
4 → 72
Calls

4 calls:

216.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
165.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
154.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
111.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 2001 to 1711 computations (14.5% saved)

simplify60.0ms (0%)

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
051673105

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

25.2b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(/.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))
25.2b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite39.0ms (0%)

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64_1123
14×*-un-lft-identity_binary64_1101
add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
add-log-exp_binary64_1140 add-cube-cbrt_binary64_1136
difference-of-squares_binary64_1070 sqrt-prod_binary64_1117 associate-/l*_binary64_1046 times-frac_binary64_1107
pow1_binary64_1162
flip--_binary64_1076 flip3--_binary64_1105 cancel-sign-sub-inv_binary64_1067
distribute-lft-out--_binary64_1053
diff-log_binary64_1193 sub-neg_binary64_1094 associate-/l/_binary64_1048 sqrt-div_binary64_1118 div-exp_binary64_1152 cbrt-undiv_binary64_1135
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:

12.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
4.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series644.0ms (0.5%)

Counts
4 → 72
Calls

4 calls:

216.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
160.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
157.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
110.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 1950 to 1660 computations (14.9% saved)

simplify86.0ms (0.1%)

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
052073272

prune1.4s (1%)

Pruning

86 alts after pruning (84 fresh and 2 done)

PrunedKeptTotal
New20484288
Fresh000
Picked000
Done022
Total20486290
Error
0.0b
Counts
290 → 86
Compiler

Compiled 5575 to 3566 computations (36% saved)

localize14.0ms (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))))
0.0b
(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)))))

rewrite67.0ms (0%)

Algorithm
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
sqrt-prod_binary64_1117 associate-/r*_binary64_1045
cancel-sign-sub-inv_binary64_1067
associate-/r/_binary64_1047
distribute-rgt-neg-in_binary64_1059 flip--_binary64_1076 flip3--_binary64_1105
pow1_binary64_1162 div-inv_binary64_1098
diff-log_binary64_1193
frac-2neg_binary64_1112 sub-neg_binary64_1094 clear-num_binary64_1100
neg-log_binary64_1194 neg-sub0_binary64_1096 associate-/l/_binary64_1048 associate--l-_binary64_1039
Counts
4 → 122
Calls

8 calls:

18.0ms
(/.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))
16.0ms
(/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
10.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
7.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series824.0ms (0.6%)

Counts
4 → 72
Calls

4 calls:

276.0ms
(/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
237.0ms
(/.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))
167.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
144.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
Compiler

Compiled 2487 to 2008 computations (19.3% saved)

simplify139.0ms (0.1%)

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 0 (85.0ms)

IterNodesCost
049475531
149475531

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

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)))
0.0b
(+.f64 b (*.f64 -2 (+.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))
25.4b
(-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b)

rewrite54.0ms (0%)

Algorithm
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
add-log-exp_binary64_1140
cbrt-undiv_binary64_1135
cube-prod_binary64_1129 unpow-prod-down_binary64_1180
pow-exp_binary64_1169 pow-to-exp_binary64_1170
pow-plus_binary64_1164 pow-prod-up_binary64_1171
cancel-sign-sub-inv_binary64_1067
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
*-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:

15.0ms
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
9.0ms
(*.f64 (*.f64 a a) (*.f64 c c))
7.0ms
(-.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 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))))

series890.0ms (0.6%)

Counts
4 → 42
Calls

4 calls:

479.0ms
(-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b)
225.0ms
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
110.0ms
(/.f64 (*.f64 a c) b)
76.0ms
(*.f64 (*.f64 a a) (*.f64 c c))
Compiler

Compiled 1893 to 1488 computations (21.4% saved)

simplify69.0ms (0%)

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
054462567

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(pow.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) 3)
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(/.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) 3)) (*.f64 2 a))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(pow.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) 3)
0.3b
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) 3))
25.2b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite42.0ms (0%)

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt_binary64_1123
21×*-un-lft-identity_binary64_1101
18×cbrt-prod_binary64_1132
12×cube-prod_binary64_1129 unpow-prod-down_binary64_1180
11×add-cube-cbrt_binary64_1136
10×difference-of-squares_binary64_1070
add-log-exp_binary64_1140
add-exp-log_binary64_1139 pow1_binary64_1162 distribute-lft-out--_binary64_1053 sqrt-prod_binary64_1117 add-cbrt-cube_binary64_1137
flip--_binary64_1076 flip3--_binary64_1105 cube-div_binary64_1130 cancel-sign-sub-inv_binary64_1067
pow-unpow_binary64_1178
diff-log_binary64_1193 cube-mult_binary64_1131 sub-neg_binary64_1094 unpow3_binary64_1167 sqr-pow_binary64_1073 cbrt-div_binary64_1133
pow-exp_binary64_1169 rem-cube-cbrt_binary64_1124 pow1/3_binary64_1183 pow-pow_binary64_1173 pow-to-exp_binary64_1170 rem-cbrt-cube_binary64_1125
Counts
4 → 89
Calls

8 calls:

10.0ms
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) 3))
9.0ms
(pow.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) 3)
9.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series839.0ms (0.6%)

Counts
4 → 73
Calls

4 calls:

335.0ms
(pow.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) 3)
172.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
166.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
164.0ms
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) 3))
Compiler

Compiled 2686 to 2305 computations (14.2% saved)

simplify95.0ms (0.1%)

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
050974268

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
25.2b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
25.2b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite37.0ms (0%)

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64_1123
12×add-log-exp_binary64_1140
10×*-un-lft-identity_binary64_1101
cancel-sign-sub-inv_binary64_1067
add-cube-cbrt_binary64_1136
diff-log_binary64_1193 difference-of-squares_binary64_1070 add-exp-log_binary64_1139 pow1_binary64_1162 sub-neg_binary64_1094 flip--_binary64_1076 flip3--_binary64_1105 add-cbrt-cube_binary64_1137
distribute-lft-out--_binary64_1053 sqrt-prod_binary64_1117
Counts
4 → 58
Calls

8 calls:

12.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
9.0ms
(-.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
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series459.0ms (0.3%)

Counts
4 → 46
Calls

4 calls:

126.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
121.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
107.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
106.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
Compiler

Compiled 2808 to 2168 computations (22.8% saved)

simplify83.0ms (0.1%)

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
048851604
148851604

prune8.2s (5.8%)

Pruning

210 alts after pruning (205 fresh and 5 done)

PrunedKeptTotal
New490135625
Fresh97079
Picked000
Done257
Total501210711
Error
0b
Counts
711 → 210
Compiler

Compiled 15932 to 10018 computations (37.1% saved)

localize16.0ms (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))))))
0.0b
(sqrt.f64 (-.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 (*.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)))))))

rewrite70.0ms (0%)

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt_binary64_1123 *-un-lft-identity_binary64_1101
34×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
27×associate-*r*_binary64_1041
24×times-frac_binary64_1107
19×add-cube-cbrt_binary64_1136
12×cbrt-unprod_binary64_1134 prod-exp_binary64_1150
10×add-log-exp_binary64_1140
pow1_binary64_1162 div-exp_binary64_1152 cbrt-undiv_binary64_1135
difference-of-squares_binary64_1070 distribute-lft-out--_binary64_1053
sqrt-prod_binary64_1117 cancel-sign-sub-inv_binary64_1067
distribute-rgt-neg-in_binary64_1059
diff-log_binary64_1193 flip--_binary64_1076 flip3--_binary64_1105 pow-prod-down_binary64_1172 associate-/r*_binary64_1045
sub-neg_binary64_1094 associate-*r/_binary64_1043 div-inv_binary64_1098 associate-/r/_binary64_1047
*-commutative_binary64_1032 frac-2neg_binary64_1112 neg-log_binary64_1194 clear-num_binary64_1100 neg-sub0_binary64_1096 associate-/l/_binary64_1048 associate-/l*_binary64_1046 associate-*l*_binary64_1042 associate--l-_binary64_1039
Counts
4 → 110
Calls

8 calls:

19.0ms
(*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))
18.0ms
(/.f64 (*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) a)
14.0ms
(-.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))))

series865.0ms (0.6%)

Counts
4 → 72
Calls

4 calls:

284.0ms
(*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))
247.0ms
(/.f64 (*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) a)
185.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
148.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))
Compiler

Compiled 2297 to 1818 computations (20.9% saved)

simplify114.0ms (0.1%)

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
049334483
149334483

localize5.0ms (0%)

rewrite0.0ms (0%)

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify11.0ms (0%)

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
000

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(/.f64 (*.f64 a c) b)
0.1b
(/.f64 (-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (pow.f64 (*.f64 a c) (+.f64 1 1)) (pow.f64 b 3))))) b) (*.f64 a 2))
0.1b
(+.f64 (/.f64 (*.f64 a c) b) (/.f64 (pow.f64 (*.f64 a c) (+.f64 1 1)) (pow.f64 b 3)))
0.0b
(+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (pow.f64 (*.f64 a c) (+.f64 1 1)) (pow.f64 b 3)))))
0.3b
(/.f64 (*.f64 a c) b)
0.4b
(/.f64 (pow.f64 (*.f64 a c) (+.f64 1 1)) (pow.f64 b 3))
0.5b
(pow.f64 (*.f64 a c) (+.f64 1 1))
25.4b
(-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (pow.f64 (*.f64 a c) (+.f64 1 1)) (pow.f64 b 3))))) b)

rewrite48.0ms (0%)

Algorithm
rewrite-expression-head
Rules
75×times-frac_binary64_1107
50×*-un-lft-identity_binary64_1101
48×add-sqr-sqrt_binary64_1123
46×add-cube-cbrt_binary64_1136
35×unpow-prod-down_binary64_1180
32×add-exp-log_binary64_1139
21×cube-prod_binary64_1129 sqr-pow_binary64_1073
15×associate-/r*_binary64_1045
14×unpow-prod-up_binary64_1179 div-exp_binary64_1152
12×pow-exp_binary64_1169 pow-unpow_binary64_1178
11×add-cbrt-cube_binary64_1137
add-log-exp_binary64_1140
pow-to-exp_binary64_1170
cube-mult_binary64_1131 pow1_binary64_1162 associate-/l*_binary64_1046 unpow3_binary64_1167
prod-exp_binary64_1150
distribute-rgt-out_binary64_1054 distribute-lft-out_binary64_1052 cbrt-undiv_binary64_1135 cancel-sign-sub-inv_binary64_1067
diff-log_binary64_1193 pow-pow_binary64_1173 frac-2neg_binary64_1112 clear-num_binary64_1100 div-inv_binary64_1098
cbrt-unprod_binary64_1134 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 pow-prod-down_binary64_1172 count-2_binary64_1049 distribute-rgt1-in_binary64_1057 distribute-lft1-in_binary64_1056
Counts
4 → 179
Calls

8 calls:

9.0ms
(/.f64 (pow.f64 (*.f64 a c) (+.f64 1 1)) (pow.f64 b 3))
8.0ms
(-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (pow.f64 (*.f64 a c) (+.f64 1 1)) (pow.f64 b 3))))) b)
7.0ms
(pow.f64 (*.f64 a c) (+.f64 1 1))
5.0ms
(/.f64 (*.f64 a c) b)
0.0ms
(+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (pow.f64 (*.f64 a c) (+.f64 1 1)) (pow.f64 b 3)))))

series903.0ms (0.6%)

Counts
4 → 42
Calls

4 calls:

491.0ms
(-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (pow.f64 (*.f64 a c) (+.f64 1 1)) (pow.f64 b 3))))) b)
225.0ms
(/.f64 (pow.f64 (*.f64 a c) (+.f64 1 1)) (pow.f64 b 3))
117.0ms
(/.f64 (*.f64 a c) b)
70.0ms
(pow.f64 (*.f64 a c) (+.f64 1 1))
Compiler

Compiled 1893 to 1506 computations (20.4% saved)

simplify82.0ms (0.1%)

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
052373745

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (-.f64 (+.f64 b (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4))) b) (*.f64 a 2))
0.1b
(+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))
0.0b
(+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4))
0.0b
(+.f64 b (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4)))
0.3b
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
0.4b
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
0.7b
(pow.f64 (*.f64 a c) 3)
25.4b
(-.f64 (+.f64 b (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4))) b)

rewrite83.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
76×add-exp-log_binary64_1139
68×times-frac_binary64_1107
43×*-un-lft-identity_binary64_1101
42×unpow-prod-down_binary64_1180
40×add-sqr-sqrt_binary64_1123
38×add-cube-cbrt_binary64_1136
28×prod-exp_binary64_1150
27×add-cbrt-cube_binary64_1137 div-exp_binary64_1152
20×sqr-pow_binary64_1073
19×associate-/r*_binary64_1045
17×pow-exp_binary64_1169
15×cube-prod_binary64_1129
13×add-log-exp_binary64_1140 pow-to-exp_binary64_1170
11×cube-mult_binary64_1131 unpow3_binary64_1167
cbrt-unprod_binary64_1134 associate-/l*_binary64_1046
pow1_binary64_1162
cbrt-undiv_binary64_1135
diff-log_binary64_1193 sum-log_binary64_1192 pow-unpow_binary64_1178 cancel-sign-sub-inv_binary64_1067
rem-cube-cbrt_binary64_1124 pow-pow_binary64_1173 frac-2neg_binary64_1112 clear-num_binary64_1100 distribute-lft-out--_binary64_1053 div-inv_binary64_1098
difference-of-squares_binary64_1070 distribute-lft-out_binary64_1052 sub-neg_binary64_1094 associate--l+_binary64_1038 flip--_binary64_1076 flip3--_binary64_1105 pow-prod-down_binary64_1172
Counts
4 → 191
Calls

8 calls:

25.0ms
(-.f64 (+.f64 b (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4))) b)
14.0ms
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
8.0ms
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
4.0ms
(pow.f64 (*.f64 a c) 3)
0.0ms
(+.f64 b (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4)))

series1.1s (0.8%)

Counts
4 → 41
Calls

4 calls:

517.0ms
(-.f64 (+.f64 b (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4))) b)
304.0ms
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
222.0ms
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
89.0ms
(pow.f64 (*.f64 a c) 3)
Compiler

Compiled 2645 to 2034 computations (23.1% saved)

simplify105.0ms (0.1%)

Algorithm
egg-herbie
Counts
232 → 232
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
051994733

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(/.f64 (+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))) (*.f64 2 a))
0.1b
(+.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 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
0.3b
(*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.7b
(pow.f64 (*.f64 (*.f64 4 a) c) 3)
31.0b
(+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))))

rewrite129.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
112×sqrt-prod_binary64_1117
97×add-sqr-sqrt_binary64_1123
78×times-frac_binary64_1107
66×*-un-lft-identity_binary64_1101
48×add-cube-cbrt_binary64_1136
42×difference-of-squares_binary64_1070
36×sqr-pow_binary64_1073
17×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
15×unpow-prod-down_binary64_1180 pow1_binary64_1162
13×associate-/l*_binary64_1046
add-log-exp_binary64_1140
distribute-lft-out--_binary64_1053
cbrt-unprod_binary64_1134 prod-exp_binary64_1150 pow-prod-down_binary64_1172 associate-/r*_binary64_1045
sqrt-div_binary64_1118
pow-exp_binary64_1169 rem-cube-cbrt_binary64_1124 pow-pow_binary64_1173 flip3-+_binary64_1104 pow-unpow_binary64_1178 associate-*r*_binary64_1041 flip-+_binary64_1075
distribute-lft-out_binary64_1052 sum-log_binary64_1192 associate-/l/_binary64_1048 associate-*r/_binary64_1043 associate-/r/_binary64_1047
distribute-rgt-neg-in_binary64_1059 *-commutative_binary64_1032 cube-prod_binary64_1129 cube-mult_binary64_1131 sqrt-undiv_binary64_1122 frac-2neg_binary64_1112 distribute-lft-in_binary64_1050 neg-log_binary64_1194 clear-num_binary64_1100 flip--_binary64_1076 flip3--_binary64_1105 neg-sub0_binary64_1096 div-inv_binary64_1098 unpow3_binary64_1167 associate-+l-_binary64_1036 +-commutative_binary64_1031 div-exp_binary64_1152 cbrt-undiv_binary64_1135 associate-*l*_binary64_1042 pow-to-exp_binary64_1170 distribute-rgt-in_binary64_1051
Counts
4 → 176
Calls

8 calls:

57.0ms
(+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))))
19.0ms
(/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
9.0ms
(*.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))

series964.0ms (0.7%)

Counts
4 → 60
Calls

4 calls:

310.0ms
(*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
306.0ms
(+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))))
231.0ms
(/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
117.0ms
(pow.f64 (*.f64 (*.f64 4 a) c) 3)
Compiler

Compiled 2704 to 2224 computations (17.8% saved)

simplify168.0ms (0.1%)

Algorithm
egg-herbie
Counts
236 → 236
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
0501412386

prune20.2s (14.2%)

Pruning

379 alts after pruning (369 fresh and 10 done)

PrunedKeptTotal
New664207871
Fresh38162200
Picked000
Done01010
Total7023791081
Error
0b
Counts
1081 → 379
Compiler

Compiled 33139 to 21167 computations (36.1% saved)

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
0.1b
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
0.2b
(/.f64 (*.f64 a 2) (/.f64 a (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))
0.3b
(/.f64 a (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))

rewrite122.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
539×times-frac_binary64_1107
324×add-sqr-sqrt_binary64_1123 *-un-lft-identity_binary64_1101
200×add-cube-cbrt_binary64_1136
113×associate-/r*_binary64_1045
62×difference-of-squares_binary64_1070 distribute-lft-out--_binary64_1053
34×sqrt-prod_binary64_1117
31×distribute-rgt-neg-in_binary64_1059
30×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
24×associate-/r/_binary64_1047
15×div-exp_binary64_1152 cbrt-undiv_binary64_1135
14×div-inv_binary64_1098
12×flip--_binary64_1076 flip3--_binary64_1105
10×add-log-exp_binary64_1140
cancel-sign-sub-inv_binary64_1067
pow1_binary64_1162 associate-/l*_binary64_1046
diff-log_binary64_1193 cbrt-unprod_binary64_1134 prod-exp_binary64_1150
frac-2neg_binary64_1112 sub-neg_binary64_1094 clear-num_binary64_1100
neg-log_binary64_1194 neg-sub0_binary64_1096 associate--l-_binary64_1039
Counts
4 → 357
Calls

8 calls:

27.0ms
(/.f64 (*.f64 a 2) (/.f64 a (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))
18.0ms
(/.f64 a (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
10.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
4.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))

series766.0ms (0.5%)

Counts
4 → 72
Calls

4 calls:

227.0ms
(/.f64 (*.f64 a 2) (/.f64 a (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))
223.0ms
(/.f64 a (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
167.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
150.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
Compiler

Compiled 2246 to 1813 computations (19.3% saved)

simplify202.0ms (0.1%)

Algorithm
egg-herbie
Counts
429 → 429
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
0495716679
1495716679

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (*.f64 a c) b)
0.2b
(/.f64 (neg.f64 (/.f64 (*.f64 a c) b)) a)
0.2b
(/.f64 (neg.f64 (/.f64 (*.f64 a c) b)) a)
0.3b
(/.f64 (*.f64 a c) b)

rewrite19.0ms (0%)

Algorithm
rewrite-expression-head
Rules
81×times-frac_binary64_1107
43×add-sqr-sqrt_binary64_1123 *-un-lft-identity_binary64_1101 add-cube-cbrt_binary64_1136
28×distribute-rgt-neg-in_binary64_1059 distribute-lft-neg-in_binary64_1058
19×associate-/l*_binary64_1046
10×div-inv_binary64_1098
add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
associate-/r*_binary64_1045
neg-mul-1_binary64_1097
div-exp_binary64_1152 cbrt-undiv_binary64_1135
add-log-exp_binary64_1140 frac-2neg_binary64_1112 pow1_binary64_1162 clear-num_binary64_1100
cbrt-unprod_binary64_1134 prod-exp_binary64_1150 distribute-neg-frac_binary64_1065 neg-sub0_binary64_1096 associate-/l/_binary64_1048 distribute-frac-neg_binary64_1064 div-sub_binary64_1106
Counts
2 → 111
Calls

4 calls:

6.0ms
(/.f64 (neg.f64 (/.f64 (*.f64 a c) b)) a)
4.0ms
(/.f64 (*.f64 a c) b)
0.0ms
(/.f64 (neg.f64 (/.f64 (*.f64 a c) b)) a)
0.0ms
(/.f64 (*.f64 a c) b)

series186.0ms (0.1%)

Counts
2 → 18
Calls

2 calls:

96.0ms
(/.f64 (*.f64 a c) b)
90.0ms
(/.f64 (neg.f64 (/.f64 (*.f64 a c) b)) a)
Compiler

Compiled 234 to 234 computations (0% saved)

simplify66.0ms (0%)

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
051262000

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
0.1b
(/.f64 (*.f64 (*.f64 a 2) (/.f64 c (log.f64 (exp.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))) a)
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
0.0b
(/.f64 c (log.f64 (exp.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))
0.1b
(exp.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
0.1b
(*.f64 (*.f64 a 2) (/.f64 c (log.f64 (exp.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))))
0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
8.1b
(log.f64 (exp.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))

rewrite64.0ms (0%)

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt_binary64_1123 *-un-lft-identity_binary64_1101
37×associate-*r*_binary64_1041
35×exp-prod_binary64_1153
33×times-frac_binary64_1107
32×log-pow_binary64_1190
29×add-cube-cbrt_binary64_1136
16×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
14×exp-sum_binary64_1147
13×pow1_binary64_1162 cancel-sign-sub-inv_binary64_1067
11×add-log-exp_binary64_1140 sqrt-prod_binary64_1117
10×difference-of-squares_binary64_1070 distribute-lft-out--_binary64_1053 log-prod_binary64_1187
cbrt-unprod_binary64_1134 prod-exp_binary64_1150
distribute-rgt-neg-in_binary64_1059
diff-log_binary64_1193 rem-exp-log_binary64_1141 sub-neg_binary64_1094 pow-prod-down_binary64_1172
exp-diff_binary64_1149 div-exp_binary64_1152 cbrt-undiv_binary64_1135
*-commutative_binary64_1032 rem-log-exp_binary64_1142 neg-log_binary64_1194 flip--_binary64_1076 flip3--_binary64_1105 associate-*r/_binary64_1043 div-inv_binary64_1098 associate-*l*_binary64_1042 log-div_binary64_1188
Counts
4 → 121
Calls

8 calls:

21.0ms
(*.f64 (*.f64 a 2) (/.f64 c (log.f64 (exp.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))))
11.0ms
(log.f64 (exp.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
11.0ms
(exp.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
0.0ms
(/.f64 c (log.f64 (exp.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))

series1.2s (0.9%)

Counts
4 → 65
Calls

4 calls:

657.0ms
(*.f64 (*.f64 a 2) (/.f64 c (log.f64 (exp.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))))
227.0ms
(log.f64 (exp.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
196.0ms
(exp.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
155.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
Compiler

Compiled 3077 to 2444 computations (20.6% saved)

simplify122.0ms (0.1%)

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
049844914
149844914

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 4 (*.f64 (*.f64 a c) (*.f64 a c))))))
0.0b
(+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 4 (*.f64 (*.f64 a c) (*.f64 a c)))))
0.0b
(/.f64 (+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 4 (*.f64 (*.f64 a c) (*.f64 a c)))))))) (*.f64 2 a))
0.0b
(-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))
0.3b
(/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 4 (*.f64 (*.f64 a c) (*.f64 a c)))))))
0.5b
(*.f64 (*.f64 a c) (*.f64 a c))
0.7b
(pow.f64 (*.f64 (*.f64 4 a) c) 3)
21.8b
(+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 4 (*.f64 (*.f64 a c) (*.f64 a c))))))))

rewrite122.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
112×sqrt-prod_binary64_1117
96×add-sqr-sqrt_binary64_1123
78×times-frac_binary64_1107
65×*-un-lft-identity_binary64_1101
49×pow1_binary64_1162
47×add-cube-cbrt_binary64_1136
42×difference-of-squares_binary64_1070
36×sqr-pow_binary64_1073
24×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
20×pow-prod-down_binary64_1172
15×unpow-prod-down_binary64_1180
13×associate-/l*_binary64_1046
11×cbrt-unprod_binary64_1134 prod-exp_binary64_1150
add-log-exp_binary64_1140
distribute-lft-out--_binary64_1053
associate-/r*_binary64_1045
pow-prod-up_binary64_1171 pow-sqr_binary64_1074 sqrt-div_binary64_1118
pow-exp_binary64_1169 rem-cube-cbrt_binary64_1124 pow-pow_binary64_1173 pow-unpow_binary64_1178
pow-plus_binary64_1164 distribute-lft-out_binary64_1052 sum-log_binary64_1192 flip3-+_binary64_1104 associate-/l/_binary64_1048 associate-/r/_binary64_1047 flip-+_binary64_1075
distribute-rgt-neg-in_binary64_1059 *-commutative_binary64_1032 cube-prod_binary64_1129 cube-mult_binary64_1131 sqrt-undiv_binary64_1122 frac-2neg_binary64_1112 neg-log_binary64_1194 clear-num_binary64_1100 flip--_binary64_1076 flip3--_binary64_1105 neg-sub0_binary64_1096 div-inv_binary64_1098 unpow3_binary64_1167 associate-+l-_binary64_1036 swap-sqr_binary64_1068 associate-*r*_binary64_1041 +-commutative_binary64_1031 div-exp_binary64_1152 cbrt-undiv_binary64_1135 associate-*l*_binary64_1042 pow2_binary64_1182 pow-to-exp_binary64_1170
Counts
4 → 188
Calls

8 calls:

59.0ms
(+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 4 (*.f64 (*.f64 a c) (*.f64 a c))))))))
19.0ms
(/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 4 (*.f64 (*.f64 a c) (*.f64 a c)))))))
7.0ms
(*.f64 (*.f64 a c) (*.f64 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))

series691.0ms (0.5%)

Counts
4 → 39
Calls

4 calls:

255.0ms
(/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 4 (*.f64 (*.f64 a c) (*.f64 a c)))))))
249.0ms
(+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 4 (*.f64 (*.f64 a c) (*.f64 a c))))))))
109.0ms
(pow.f64 (*.f64 (*.f64 4 a) c) 3)
78.0ms
(*.f64 (*.f64 a c) (*.f64 a c))
Compiler

Compiled 1875 to 1592 computations (15.1% saved)

simplify112.0ms (0.1%)

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
054069142

localize34.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b))
0.1b
(/.f64 (+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))) (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))))))))) (*.f64 2 a))
0.1b
(+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))) (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))))))
0.0b
(-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))
0.3b
(*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))
0.5b
(*.f64 (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))) (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))))
0.7b
(pow.f64 (*.f64 (*.f64 4 a) c) 3)
31.0b
(+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))) (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b))))))))))

rewrite126.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
142×pow1_binary64_1162
77×pow-prod-down_binary64_1172
60×sqrt-pow1_binary64_1119
17×pow-prod-up_binary64_1171 add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
16×associate-*r/_binary64_1043
14×*-un-lft-identity_binary64_1101
12×add-sqr-sqrt_binary64_1123 sqrt-div_binary64_1118 pow1/2_binary64_1181
11×pow-sqr_binary64_1074
10×add-cube-cbrt_binary64_1136
add-log-exp_binary64_1140 flip3-+_binary64_1104 flip-+_binary64_1075
cbrt-unprod_binary64_1134 prod-exp_binary64_1150 associate-*r*_binary64_1041
associate-*l*_binary64_1042
frac-times_binary64_1111 sqrt-prod_binary64_1117 swap-sqr_binary64_1068
pow-exp_binary64_1169 rem-cube-cbrt_binary64_1124 pow-pow_binary64_1173 pow-unpow_binary64_1178
*-commutative_binary64_1032 distribute-lft-out_binary64_1052 sum-log_binary64_1192 associate-*l/_binary64_1044
distribute-rgt-neg-in_binary64_1059 pow-plus_binary64_1164 cube-prod_binary64_1129 cube-mult_binary64_1131 unpow-prod-down_binary64_1180 rem-square-sqrt_binary64_1113 distribute-lft-in_binary64_1050 neg-log_binary64_1194 neg-sub0_binary64_1096 unpow3_binary64_1167 associate-+l-_binary64_1036 +-commutative_binary64_1031 unswap-sqr_binary64_1069 sqr-pow_binary64_1073 sqrt-unprod_binary64_1121 pow2_binary64_1182 pow-to-exp_binary64_1170 distribute-rgt-in_binary64_1051
Counts
4 → 136
Calls

8 calls:

57.0ms
(+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))) (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b))))))))))
26.0ms
(*.f64 (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))) (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))))
11.0ms
(*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))
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))

series1.1s (0.8%)

Counts
4 → 60
Calls

4 calls:

368.0ms
(*.f64 (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))) (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))))
312.0ms
(+.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))) (sqrt.f64 (*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b))))))))))
312.0ms
(*.f64 (*.f64 a c) (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)))
125.0ms
(pow.f64 (*.f64 (*.f64 4 a) c) 3)
Compiler

Compiled 3925 to 3081 computations (21.5% saved)

simplify100.0ms (0.1%)

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
052664260

prune40.0s (28.1%)

Pruning

689 alts after pruning (677 fresh and 12 done)

PrunedKeptTotal
New8233441167
Fresh31333364
Picked000
Done31215
Total8576891546
Error
0b
Counts
1546 → 689
Compiler

Compiled 23844 to 13185 computations (44.7% saved)

simplify1.1s (0.7%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (13.0ms)

IterNodesCost
0530070764

regimes15.3s (10.7%)

Compiler

Compiled 183048 to 130928 computations (28.5% saved)

bsearch0.0ms (0%)

regimes358.0ms (0.3%)

Compiler

Compiled 3108 to 2589 computations (16.7% saved)

bsearch0.0ms (0%)

regimes181.0ms (0.1%)

Compiler

Compiled 1209 to 1149 computations (5% saved)

bsearch0.0ms (0%)

regimes25.0ms (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch0.0ms (0%)

regimes23.0ms (0%)

Accuracy

Total 0.1b remaining (100%)

Threshold costs 0.1b (100%)

Compiler

Compiled 12 to 42 computations (-250% saved)

bsearch4.0ms (0%)

Compiler

Compiled 41 to 44 computations (-7.3% saved)

simplify5.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
09860
19860

end0.0ms (0%)

sample39.8s (27.9%)

Algorithm
intervals
Results
374.0ms3820×body256valid
278.0ms8826×pre128true
215.0ms1476×body512valid
140.0ms2704×body128valid
41.0ms826×body128nan
Compiler

Compiled 45882 to 32858 computations (28.4% saved)

Pareto

0.9163450864471888

Profiling

Loading profile data...