Details

Time bar (total: 55.7s)

analyze7.0ms (0%)

Algorithm
search
Search
TrueOtherFalseIter
0%74.6%25.4%0
0%74.6%25.4%1
37.3%37.3%25.4%2
37.3%18.7%44%3
46.7%9.3%44%4
46.7%4.7%48.7%5
49%2.3%48.7%6
49%1.2%49.8%7
49.6%0.6%49.8%8
49.9%0.3%49.8%9
49.9%0.1%50%10
49.9%0.1%50.1%11
49.9%0%50.1%12
49.9%0%50.1%13
49.9%0%50.1%14
Compiler

Compiled 7 to 6 computations (14.3% saved)

sample33.0ms (0.1%)

Algorithm
intervals
Results
16.0ms127×body1024valid
4.0ms66×body512valid
3.0ms256×pre128true
1.0ms35×body256valid
1.0msbody2048valid
0.0ms20×body128valid
Compiler

Compiled 11 to 11 computations (0% saved)

simplify96.0ms (0.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
096
196

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
57.8b
Counts
2 → 1
Compiler

Compiled 4 to 4 computations (0% saved)

localize3.0ms (0%)

Local error

Found 2 expressions with local error:

5.2b
(-.f64 (exp.f64 x) 1)
5.2b
(-.f64 (exp.f64 x) 1)

rewrite7.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64_1123
*-un-lft-identity_binary64_1101
add-log-exp_binary64_1140 cancel-sign-sub-inv_binary64_1067
difference-of-squares_binary64_1070 add-cube-cbrt_binary64_1136
diff-log_binary64_1193 add-exp-log_binary64_1139 pow1_binary64_1162 sub-neg_binary64_1094 difference-of-sqr-1_binary64_1071 distribute-lft-out--_binary64_1053 flip--_binary64_1076 flip3--_binary64_1105 add-cbrt-cube_binary64_1137
Counts
1 → 18
Calls

2 calls:

5.0ms
(-.f64 (exp.f64 x) 1)
0.0ms
(-.f64 (exp.f64 x) 1)

series17.0ms (0%)

Counts
1 → 6
Calls

1 calls:

17.0ms
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 56 to 50 computations (10.7% saved)

simplify87.0ms (0.2%)

Algorithm
egg-herbie
Counts
24 → 24
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
04922232
14922232

prune53.0ms (0.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New101424
Fresh000
Picked000
Done011
Total101525
Error
0.0b
Counts
25 → 15
Compiler

Compiled 269 to 195 computations (27.5% saved)

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
0.0b
(*.f64 x (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 x 1/24))))))
0.0b
(+.f64 x (*.f64 x (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 x 1/24)))))))
0.0b
(+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 x 1/24))))
0.0b
(*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
0.0b
(+.f64 1/6 (*.f64 x 1/24))
0.3b
(*.f64 x (+.f64 1/6 (*.f64 x 1/24)))
0.3b
(*.f64 x 1/24)

rewrite24.0ms (0%)

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt_binary64_1123
10×*-un-lft-identity_binary64_1101 add-exp-log_binary64_1139 pow1_binary64_1162 add-cube-cbrt_binary64_1136 add-cbrt-cube_binary64_1137
associate-*r*_binary64_1041 associate-*l*_binary64_1042
add-log-exp_binary64_1140
associate-*r/_binary64_1043
*-commutative_binary64_1032 cbrt-unprod_binary64_1134 prod-exp_binary64_1150 flip3-+_binary64_1104 pow-prod-down_binary64_1172 flip-+_binary64_1075 unswap-sqr_binary64_1069
distribute-lft-in_binary64_1050 distribute-rgt-in_binary64_1051
sum-log_binary64_1192 +-commutative_binary64_1031
Counts
4 → 73
Calls

8 calls:

6.0ms
(*.f64 x (+.f64 1/6 (*.f64 x 1/24)))
6.0ms
(*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
4.0ms
(*.f64 x 1/24)
3.0ms
(+.f64 1/6 (*.f64 x 1/24))
0.0ms
(+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 x 1/24))))

series127.0ms (0.2%)

Counts
4 → 20
Calls

4 calls:

47.0ms
(*.f64 x (+.f64 1/6 (*.f64 x 1/24)))
33.0ms
(*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
31.0ms
(+.f64 1/6 (*.f64 x 1/24))
15.0ms
(*.f64 x 1/24)
Compiler

Compiled 462 to 347 computations (24.9% saved)

simplify83.0ms (0.1%)

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
048841083
148841083

localize4.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 1/2 (*.f64 x x))
0.0b
(+.f64 x (*.f64 1/2 (*.f64 x x)))
0.0b
(+.f64 x (*.f64 1/2 (*.f64 x x)))
0.0b
(*.f64 1/2 (*.f64 x x))

rewrite11.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-exp-log_binary64_1139 pow1_binary64_1162 add-cbrt-cube_binary64_1137
add-sqr-sqrt_binary64_1123 add-log-exp_binary64_1140
cbrt-unprod_binary64_1134 *-un-lft-identity_binary64_1101 prod-exp_binary64_1150 add-cube-cbrt_binary64_1136 pow-prod-down_binary64_1172 associate-*l*_binary64_1042
*-commutative_binary64_1032 sum-log_binary64_1192 flip3-+_binary64_1104 associate-*r*_binary64_1041 +-commutative_binary64_1031 flip-+_binary64_1075 unswap-sqr_binary64_1069
Counts
2 → 30
Calls

4 calls:

6.0ms
(*.f64 1/2 (*.f64 x x))
3.0ms
(+.f64 x (*.f64 1/2 (*.f64 x x)))
0.0ms
(+.f64 x (*.f64 1/2 (*.f64 x x)))
0.0ms
(*.f64 1/2 (*.f64 x x))

series74.0ms (0.1%)

Counts
2 → 9
Calls

2 calls:

47.0ms
(+.f64 x (*.f64 1/2 (*.f64 x x)))
27.0ms
(*.f64 1/2 (*.f64 x x))
Compiler

Compiled 95 to 83 computations (12.6% saved)

simplify88.0ms (0.2%)

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
04914390
14914390

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

5.2b
(-.f64 (exp.f64 x) 1)
5.2b
(-.f64 (exp.f64 x) 1)

rewrite6.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64_1123
*-un-lft-identity_binary64_1101
add-log-exp_binary64_1140 cancel-sign-sub-inv_binary64_1067
difference-of-squares_binary64_1070 add-cube-cbrt_binary64_1136
diff-log_binary64_1193 add-exp-log_binary64_1139 pow1_binary64_1162 sub-neg_binary64_1094 difference-of-sqr-1_binary64_1071 distribute-lft-out--_binary64_1053 flip--_binary64_1076 flip3--_binary64_1105 add-cbrt-cube_binary64_1137
Counts
1 → 18
Calls

2 calls:

4.0ms
(-.f64 (exp.f64 x) 1)
0.0ms
(-.f64 (exp.f64 x) 1)

series17.0ms (0%)

Counts
1 → 6
Calls

1 calls:

17.0ms
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 72 to 66 computations (8.3% saved)

simplify76.0ms (0.1%)

Algorithm
egg-herbie
Counts
24 → 24
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
04922232
14922232

localize6.0ms (0%)

Local error

Found 6 expressions with local error:

5.2b
(-.f64 (exp.f64 x) 1)
0.1b
(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
0.0b
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
0.0b
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
0.1b
(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
5.2b
(-.f64 (exp.f64 x) 1)

rewrite24.0ms (0%)

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt_binary64_1123
25×*-un-lft-identity_binary64_1101
20×cbrt-prod_binary64_1132
14×cube-prod_binary64_1129 unpow-prod-down_binary64_1180
10×difference-of-squares_binary64_1070 add-cube-cbrt_binary64_1136
add-log-exp_binary64_1140 difference-of-sqr-1_binary64_1071 distribute-lft-out--_binary64_1053
add-exp-log_binary64_1139 pow1_binary64_1162 cube-div_binary64_1130 add-cbrt-cube_binary64_1137
flip--_binary64_1076 flip3--_binary64_1105 pow-unpow_binary64_1178 cancel-sign-sub-inv_binary64_1067
cube-mult_binary64_1131 unpow3_binary64_1167 sqr-pow_binary64_1073 cbrt-div_binary64_1133
diff-log_binary64_1193 pow-exp_binary64_1169 rem-cube-cbrt_binary64_1124 pow1/3_binary64_1183 pow-pow_binary64_1173 sub-neg_binary64_1094 pow-to-exp_binary64_1170 rem-cbrt-cube_binary64_1125
Counts
3 → 82
Calls

6 calls:

8.0ms
(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
6.0ms
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
5.0ms
(-.f64 (exp.f64 x) 1)
0.0ms
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
0.0ms
(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))

series87.0ms (0.2%)

Counts
3 → 18
Calls

3 calls:

50.0ms
(pow.f64 (-.f64 (exp.f64 x) 1) 3)
19.0ms
(-.f64 (exp.f64 x) 1)
17.0ms
(cbrt.f64 (pow.f64 (-.f64 (exp.f64 x) 1) 3))
Compiler

Compiled 216 to 198 computations (8.3% saved)

simplify91.0ms (0.2%)

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
049781239
149781239

localize7.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
0.0b
(+.f64 1 (sqrt.f64 (exp.f64 x)))
0.0b
(sqrt.f64 (exp.f64 x))
0.0b
(sqrt.f64 (exp.f64 x))
0.0b
(sqrt.f64 (exp.f64 x))
0.0b
(+.f64 1 (sqrt.f64 (exp.f64 x)))
0.0b
(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
5.3b
(+.f64 -1 (sqrt.f64 (exp.f64 x)))

rewrite28.0ms (0%)

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity_binary64_1101
13×add-sqr-sqrt_binary64_1123
add-log-exp_binary64_1140 flip3-+_binary64_1104 add-cube-cbrt_binary64_1136 flip-+_binary64_1075
pow1_binary64_1162
distribute-lft-out_binary64_1052 add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
sqrt-prod_binary64_1117 associate-*l*_binary64_1042
frac-times_binary64_1111 sqrt-pow1_binary64_1119 associate-*r*_binary64_1041
exp-prod_binary64_1153
sum-log_binary64_1192 associate-*r/_binary64_1043 +-commutative_binary64_1031 associate-*l/_binary64_1044
*-commutative_binary64_1032 rem-sqrt-square_binary64_1114 cbrt-unprod_binary64_1134 prod-exp_binary64_1150 distribute-lft-in_binary64_1050 pow-prod-down_binary64_1172 unswap-sqr_binary64_1069 distribute-rgt-in_binary64_1051 pow1/2_binary64_1181
Counts
4 → 72
Calls

8 calls:

11.0ms
(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
4.0ms
(+.f64 1 (sqrt.f64 (exp.f64 x)))
4.0ms
(+.f64 -1 (sqrt.f64 (exp.f64 x)))
3.0ms
(sqrt.f64 (exp.f64 x))
0.0ms
(sqrt.f64 (exp.f64 x))

series126.0ms (0.2%)

Counts
4 → 24
Calls

4 calls:

54.0ms
(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
28.0ms
(+.f64 -1 (sqrt.f64 (exp.f64 x)))
23.0ms
(+.f64 1 (sqrt.f64 (exp.f64 x)))
21.0ms
(sqrt.f64 (exp.f64 x))
Compiler

Compiled 412 to 336 computations (18.4% saved)

simplify73.0ms (0.1%)

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
053881171

prune3.2s (5.7%)

Pruning

144 alts after pruning (138 fresh and 6 done)

PrunedKeptTotal
New221131352
Fresh279
Picked000
Done066
Total223144367
Error
0.0b
Counts
367 → 144
Compiler

Compiled 5861 to 4074 computations (30.5% saved)

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (exp.f64 x))
0.0b
(+.f64 (*.f64 x 1/2) (+.f64 (*.f64 (*.f64 x x) (+.f64 1/8 (*.f64 x 1/48))) (*.f64 1/384 (pow.f64 x 4))))
0.0b
(+.f64 (*.f64 (*.f64 x x) (+.f64 1/8 (*.f64 x 1/48))) (*.f64 1/384 (pow.f64 x 4)))
0.0b
(+.f64 1/8 (*.f64 x 1/48))
0.0b
(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 (*.f64 x 1/2) (+.f64 (*.f64 (*.f64 x x) (+.f64 1/8 (*.f64 x 1/48))) (*.f64 1/384 (pow.f64 x 4)))))
0.0b
(*.f64 (*.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))
0.1b
(*.f64 1/384 (pow.f64 x 4))
0.3b
(*.f64 x 1/48)

rewrite44.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt_binary64_1123
18×add-exp-log_binary64_1139
16×associate-*r*_binary64_1041
15×*-un-lft-identity_binary64_1101 add-cbrt-cube_binary64_1137
13×pow1_binary64_1162
12×add-cube-cbrt_binary64_1136 associate-*l*_binary64_1042
prod-exp_binary64_1150
flip3-+_binary64_1104 flip-+_binary64_1075
cbrt-unprod_binary64_1134 unswap-sqr_binary64_1069
pow-prod-down_binary64_1172
*-commutative_binary64_1032 unpow-prod-down_binary64_1180 frac-times_binary64_1111 add-log-exp_binary64_1140 associate-*r/_binary64_1043
distribute-lft-out_binary64_1052 distribute-lft-in_binary64_1050 associate-*l/_binary64_1044 sqr-pow_binary64_1073 distribute-rgt-in_binary64_1051
pow-exp_binary64_1169 sqrt-prod_binary64_1117 pow-to-exp_binary64_1170
Counts
4 → 96
Calls

8 calls:

15.0ms
(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 (*.f64 x 1/2) (+.f64 (*.f64 (*.f64 x x) (+.f64 1/8 (*.f64 x 1/48))) (*.f64 1/384 (pow.f64 x 4)))))
8.0ms
(*.f64 (*.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))
6.0ms
(*.f64 1/384 (pow.f64 x 4))
4.0ms
(*.f64 x 1/48)
0.0ms
(+.f64 1/8 (*.f64 x 1/48))

series204.0ms (0.4%)

Counts
4 → 24
Calls

4 calls:

83.0ms
(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 (*.f64 x 1/2) (+.f64 (*.f64 (*.f64 x x) (+.f64 1/8 (*.f64 x 1/48))) (*.f64 1/384 (pow.f64 x 4)))))
63.0ms
(*.f64 (*.f64 x x) (+.f64 1/8 (*.f64 x 1/48)))
39.0ms
(*.f64 1/384 (pow.f64 x 4))
19.0ms
(*.f64 x 1/48)
Compiler

Compiled 861 to 688 computations (20.1% saved)

simplify98.0ms (0.2%)

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
049132566
149132566

localize3.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 1/2 (*.f64 x x))
0.0b
(*.f64 1/2 (*.f64 x x))

rewrite7.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-exp-log_binary64_1139 pow1_binary64_1162 add-cbrt-cube_binary64_1137
add-sqr-sqrt_binary64_1123 cbrt-unprod_binary64_1134 prod-exp_binary64_1150 pow-prod-down_binary64_1172 associate-*l*_binary64_1042
*-un-lft-identity_binary64_1101 add-cube-cbrt_binary64_1136
*-commutative_binary64_1032 add-log-exp_binary64_1140 associate-*r*_binary64_1041 unswap-sqr_binary64_1069
Counts
1 → 19
Calls

2 calls:

6.0ms
(*.f64 1/2 (*.f64 x x))
0.0ms
(*.f64 1/2 (*.f64 x x))

series28.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

28.0ms
(*.f64 1/2 (*.f64 x x))
Compiler

Compiled 30 to 30 computations (0% saved)

simplify66.0ms (0.1%)

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
05148179

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (cbrt.f64 (pow.f64 (*.f64 x 1/24) 3))))))
0.0b
(*.f64 x (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (cbrt.f64 (pow.f64 (*.f64 x 1/24) 3)))))))
0.0b
(+.f64 x (*.f64 x (*.f64 x (+.f64 1/2 (*.f64 x (+.f64 1/6 (cbrt.f64 (pow.f64 (*.f64 x 1/24) 3))))))))
0.0b
(+.f64 1/2 (*.f64 x (+.f64 1/6 (cbrt.f64 (pow.f64 (*.f64 x 1/24) 3)))))
0.2b
(pow.f64 (*.f64 x 1/24) 3)
0.3b
(*.f64 x (+.f64 1/6 (cbrt.f64 (pow.f64 (*.f64 x 1/24) 3))))
0.3b
(*.f64 x 1/24)
39.9b
(cbrt.f64 (pow.f64 (*.f64 x 1/24) 3))

rewrite27.0ms (0%)

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64_1123
12×*-un-lft-identity_binary64_1101
11×add-exp-log_binary64_1139 pow1_binary64_1162 add-cbrt-cube_binary64_1137
10×add-cube-cbrt_binary64_1136
cbrt-prod_binary64_1132
associate-*r*_binary64_1041
associate-*l*_binary64_1042
add-log-exp_binary64_1140
cbrt-unprod_binary64_1134 prod-exp_binary64_1150 pow-unpow_binary64_1178 pow-prod-down_binary64_1172
*-commutative_binary64_1032 pow-exp_binary64_1169 cube-prod_binary64_1129 cube-mult_binary64_1131 rem-cube-cbrt_binary64_1124 unpow-prod-down_binary64_1180 pow-pow_binary64_1173 associate-*r/_binary64_1043 unpow3_binary64_1167 unswap-sqr_binary64_1069 sqr-pow_binary64_1073
pow1/3_binary64_1183 distribute-lft-out_binary64_1052 distribute-lft-in_binary64_1050 flip3-+_binary64_1104 flip-+_binary64_1075 pow-to-exp_binary64_1170 distribute-rgt-in_binary64_1051 rem-cbrt-cube_binary64_1125
Counts
4 → 80
Calls

8 calls:

10.0ms
(*.f64 x (+.f64 1/6 (cbrt.f64 (pow.f64 (*.f64 x 1/24) 3))))
4.0ms
(*.f64 x 1/24)
4.0ms
(pow.f64 (*.f64 x 1/24) 3)
3.0ms
(cbrt.f64 (pow.f64 (*.f64 x 1/24) 3))
0.0ms
(+.f64 1/2 (*.f64 x (+.f64 1/6 (cbrt.f64 (pow.f64 (*.f64 x 1/24) 3)))))

series151.0ms (0.3%)

Counts
4 → 15
Calls

4 calls:

65.0ms
(*.f64 x (+.f64 1/6 (cbrt.f64 (pow.f64 (*.f64 x 1/24) 3))))
36.0ms
(pow.f64 (*.f64 x 1/24) 3)
29.0ms
(cbrt.f64 (pow.f64 (*.f64 x 1/24) 3))
20.0ms
(*.f64 x 1/24)
Compiler

Compiled 465 to 360 computations (22.6% saved)

simplify62.0ms (0.1%)

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
04941805
14941805

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

5.2b
(-.f64 (exp.f64 x) 1)
0.1b
(cbrt.f64 (*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (-.f64 (exp.f64 x) 1) 2)))
0.0b
(*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (-.f64 (exp.f64 x) 1) 2))
0.0b
(pow.f64 (-.f64 (exp.f64 x) 1) 2)
0.0b
(pow.f64 (-.f64 (exp.f64 x) 1) 2)
0.1b
(cbrt.f64 (*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (-.f64 (exp.f64 x) 1) 2)))
5.2b
(-.f64 (exp.f64 x) 1)
5.2b
(-.f64 (exp.f64 x) 1)

rewrite30.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64_1123
17×*-un-lft-identity_binary64_1101
add-log-exp_binary64_1140 add-cube-cbrt_binary64_1136
unpow-prod-down_binary64_1180
difference-of-squares_binary64_1070 cancel-sign-sub-inv_binary64_1067
add-exp-log_binary64_1139 pow1_binary64_1162
add-cbrt-cube_binary64_1137
difference-of-sqr-1_binary64_1071 distribute-lft-out--_binary64_1053 flip--_binary64_1076 flip3--_binary64_1105 pow-unpow_binary64_1178
diff-log_binary64_1193 sub-neg_binary64_1094 associate-*l/_binary64_1044 unpow2_binary64_1166 cbrt-div_binary64_1133
pow-exp_binary64_1169 pow1/3_binary64_1183 pow-pow_binary64_1173 cube-unmult_binary64_1138 sqr-pow_binary64_1073 pow-to-exp_binary64_1170 cbrt-prod_binary64_1132 rem-cbrt-cube_binary64_1125
Counts
4 → 70
Calls

8 calls:

11.0ms
(cbrt.f64 (*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (-.f64 (exp.f64 x) 1) 2)))
5.0ms
(pow.f64 (-.f64 (exp.f64 x) 1) 2)
5.0ms
(-.f64 (exp.f64 x) 1)
4.0ms
(-.f64 (exp.f64 x) 1)
0.0ms
(pow.f64 (-.f64 (exp.f64 x) 1) 2)

series90.0ms (0.2%)

Counts
4 → 24
Calls

4 calls:

36.0ms
(pow.f64 (-.f64 (exp.f64 x) 1) 2)
19.0ms
(cbrt.f64 (*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (-.f64 (exp.f64 x) 1) 2)))
18.0ms
(-.f64 (exp.f64 x) 1)
18.0ms
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 410 to 350 computations (14.6% saved)

simplify69.0ms (0.1%)

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
052561004

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)) (sqrt.f64 (-.f64 (exp.f64 x) 1))) 3))
0.0b
(pow.f64 (*.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)) (sqrt.f64 (-.f64 (exp.f64 x) 1))) 3)
0.0b
(sqrt.f64 (-.f64 (exp.f64 x) 1))
0.0b
(sqrt.f64 (-.f64 (exp.f64 x) 1))
0.0b
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)) (sqrt.f64 (-.f64 (exp.f64 x) 1))) 3))
0.0b
(*.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)) (sqrt.f64 (-.f64 (exp.f64 x) 1)))
5.2b
(-.f64 (exp.f64 x) 1)
5.2b
(-.f64 (exp.f64 x) 1)

rewrite44.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt_binary64_1123
42×sqrt-prod_binary64_1117
41×*-un-lft-identity_binary64_1101
24×sqrt-div_binary64_1118
19×pow1_binary64_1162
16×swap-sqr_binary64_1068
15×add-cube-cbrt_binary64_1136
14×difference-of-squares_binary64_1070 flip--_binary64_1076 flip3--_binary64_1105
10×associate-*r*_binary64_1041 associate-*l*_binary64_1042
frac-times_binary64_1111 add-log-exp_binary64_1140 sqrt-pow1_binary64_1119 difference-of-sqr-1_binary64_1071 distribute-lft-out--_binary64_1053 cube-div_binary64_1130 cbrt-prod_binary64_1132 cbrt-div_binary64_1133 pow1/2_binary64_1181
add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137 cancel-sign-sub-inv_binary64_1067
pow-prod-up_binary64_1171
associate-*r/_binary64_1043 unswap-sqr_binary64_1069 associate-*l/_binary64_1044
pow-sqr_binary64_1074 pow-prod-down_binary64_1172
diff-log_binary64_1193 rem-sqrt-square_binary64_1114 sub-neg_binary64_1094
pow-plus_binary64_1164 *-commutative_binary64_1032 cube-prod_binary64_1129 cube-mult_binary64_1131 cbrt-unprod_binary64_1134 pow1/3_binary64_1183 unpow-prod-down_binary64_1180 prod-exp_binary64_1150 rem-square-sqrt_binary64_1113 unpow3_binary64_1167 sqr-abs_binary64_1116 sqr-pow_binary64_1073 sqrt-unprod_binary64_1121 pow2_binary64_1182 rem-cbrt-cube_binary64_1125
Counts
4 → 135
Calls

8 calls:

17.0ms
(*.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)) (sqrt.f64 (-.f64 (exp.f64 x) 1)))
5.0ms
(-.f64 (exp.f64 x) 1)
5.0ms
(-.f64 (exp.f64 x) 1)
4.0ms
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)) (sqrt.f64 (-.f64 (exp.f64 x) 1))) 3))
0.0ms
(sqrt.f64 (-.f64 (exp.f64 x) 1))

series79.0ms (0.1%)

Counts
4 → 24
Calls

4 calls:

23.0ms
(-.f64 (exp.f64 x) 1)
20.0ms
(-.f64 (exp.f64 x) 1)
18.0ms
(*.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)) (sqrt.f64 (-.f64 (exp.f64 x) 1)))
18.0ms
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)) (sqrt.f64 (-.f64 (exp.f64 x) 1))) 3))
Compiler

Compiled 408 to 360 computations (11.8% saved)

simplify94.0ms (0.2%)

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
049341986
149341986

prune10.9s (19.5%)

Pruning

284 alts after pruning (275 fresh and 9 done)

PrunedKeptTotal
New338152490
Fresh10123133
Picked000
Done2911
Total350284634
Error
0.0b
Counts
634 → 284
Compiler

Compiled 12568 to 9290 computations (26.1% saved)

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 1/8 (*.f64 x 1/48))
0.0b
(sqrt.f64 (exp.f64 x))
0.0b
(+.f64 (*.f64 x 1/2) (+.f64 (/.f64 (*.f64 (*.f64 x x) (-.f64 1/64 (*.f64 x (*.f64 1/2304 x)))) (-.f64 1/8 (*.f64 x 1/48))) (*.f64 1/384 (pow.f64 x 4))))
0.0b
(+.f64 (/.f64 (*.f64 (*.f64 x x) (-.f64 1/64 (*.f64 x (*.f64 1/2304 x)))) (-.f64 1/8 (*.f64 x 1/48))) (*.f64 1/384 (pow.f64 x 4)))
0.1b
(*.f64 x (*.f64 1/2304 x))
0.1b
(*.f64 1/384 (pow.f64 x 4))
0.3b
(*.f64 x 1/48)
0.4b
(*.f64 1/2304 x)

rewrite29.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64_1123
18×add-exp-log_binary64_1139
15×add-cbrt-cube_binary64_1137
14×associate-*r*_binary64_1041
13×pow1_binary64_1162
12×*-un-lft-identity_binary64_1101 add-cube-cbrt_binary64_1136 associate-*l*_binary64_1042
prod-exp_binary64_1150
cbrt-unprod_binary64_1134
pow-prod-down_binary64_1172 unswap-sqr_binary64_1069
*-commutative_binary64_1032 unpow-prod-down_binary64_1180 add-log-exp_binary64_1140
sqr-pow_binary64_1073
pow-exp_binary64_1169 pow-to-exp_binary64_1170
Counts
4 → 79
Calls

8 calls:

6.0ms
(*.f64 x (*.f64 1/2304 x))
6.0ms
(*.f64 1/384 (pow.f64 x 4))
4.0ms
(*.f64 x 1/48)
4.0ms
(*.f64 1/2304 x)
0.0ms
(+.f64 (/.f64 (*.f64 (*.f64 x x) (-.f64 1/64 (*.f64 x (*.f64 1/2304 x)))) (-.f64 1/8 (*.f64 x 1/48))) (*.f64 1/384 (pow.f64 x 4)))

series115.0ms (0.2%)

Counts
4 → 12
Calls

4 calls:

42.0ms
(*.f64 1/384 (pow.f64 x 4))
30.0ms
(*.f64 x (*.f64 1/2304 x))
22.0ms
(*.f64 1/2304 x)
21.0ms
(*.f64 x 1/48)
Compiler

Compiled 792 to 630 computations (20.5% saved)

simplify74.0ms (0.1%)

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
04982680
14982680

localize3.0ms (0%)

rewrite1.0ms (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

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(pow.f64 (+.f64 x (*.f64 1/2 (*.f64 x x))) 2)
0.0b
(*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (+.f64 x (*.f64 1/2 (*.f64 x x))) 2))
0.0b
(*.f64 1/2 (*.f64 x x))
0.0b
(+.f64 x (*.f64 1/2 (*.f64 x x)))
0.0b
(*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (+.f64 x (*.f64 1/2 (*.f64 x x))) 2))
0.0b
(pow.f64 (+.f64 x (*.f64 1/2 (*.f64 x x))) 2)
0.1b
(cbrt.f64 (*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (+.f64 x (*.f64 1/2 (*.f64 x x))) 2)))
5.2b
(-.f64 (exp.f64 x) 1)

rewrite40.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt_binary64_1123
16×*-un-lft-identity_binary64_1101
10×add-exp-log_binary64_1139 add-cube-cbrt_binary64_1136
associate-*r*_binary64_1041
unpow-prod-down_binary64_1180 associate-*l*_binary64_1042
add-log-exp_binary64_1140 add-cbrt-cube_binary64_1137
pow1_binary64_1162
difference-of-squares_binary64_1070 unswap-sqr_binary64_1069 associate-*l/_binary64_1044
prod-exp_binary64_1150 flip--_binary64_1076 flip3--_binary64_1105 pow-unpow_binary64_1178 cancel-sign-sub-inv_binary64_1067 sqr-pow_binary64_1073 unpow2_binary64_1166
pow-exp_binary64_1169 difference-of-sqr-1_binary64_1071 distribute-lft-out--_binary64_1053 pow-to-exp_binary64_1170 cbrt-div_binary64_1133
diff-log_binary64_1193 *-commutative_binary64_1032 cbrt-unprod_binary64_1134 pow1/3_binary64_1183 pow-pow_binary64_1173 sub-neg_binary64_1094 cbrt-prod_binary64_1132
Counts
4 → 80
Calls

8 calls:

13.0ms
(*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (+.f64 x (*.f64 1/2 (*.f64 x x))) 2))
9.0ms
(cbrt.f64 (*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (+.f64 x (*.f64 1/2 (*.f64 x x))) 2)))
7.0ms
(-.f64 (exp.f64 x) 1)
4.0ms
(pow.f64 (+.f64 x (*.f64 1/2 (*.f64 x x))) 2)
0.0ms
(+.f64 x (*.f64 1/2 (*.f64 x x)))

series270.0ms (0.5%)

Counts
4 → 26
Calls

4 calls:

109.0ms
(*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (+.f64 x (*.f64 1/2 (*.f64 x x))) 2))
73.0ms
(cbrt.f64 (*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (+.f64 x (*.f64 1/2 (*.f64 x x))) 2)))
71.0ms
(pow.f64 (+.f64 x (*.f64 1/2 (*.f64 x x))) 2)
16.0ms
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 802 to 651 computations (18.8% saved)

simplify82.0ms (0.1%)

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
050501925

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 (-.f64 1 (exp.f64 x)) (-.f64 -1 (sqrt.f64 (exp.f64 x))))
0.0b
(-.f64 -1 (sqrt.f64 (exp.f64 x)))
0.0b
(sqrt.f64 (exp.f64 x))
0.0b
(sqrt.f64 (exp.f64 x))
0.0b
(/.f64 (-.f64 1 (exp.f64 x)) (-.f64 -1 (sqrt.f64 (exp.f64 x))))
0.0b
(-.f64 -1 (sqrt.f64 (exp.f64 x)))
0.0b
(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 -1 (sqrt.f64 (exp.f64 x)))))
5.2b
(-.f64 1 (exp.f64 x))

rewrite70.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt_binary64_1123
108×*-un-lft-identity_binary64_1101
73×times-frac_binary64_1107
56×difference-of-squares_binary64_1070
42×associate-*r*_binary64_1041
35×add-cube-cbrt_binary64_1136
28×distribute-lft-out--_binary64_1053
18×sqrt-prod_binary64_1117
11×add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
cancel-sign-sub-inv_binary64_1067
add-log-exp_binary64_1140
pow1_binary64_1162 associate-/l*_binary64_1046 associate-/r*_binary64_1045
flip--_binary64_1076 flip3--_binary64_1105 associate-*l*_binary64_1042
associate-/r/_binary64_1047
diff-log_binary64_1193 cbrt-unprod_binary64_1134 frac-times_binary64_1111 prod-exp_binary64_1150 distribute-lft-out_binary64_1052 sub-neg_binary64_1094 flip3-+_binary64_1104 associate-/l/_binary64_1048 div-inv_binary64_1098 div-exp_binary64_1152 cbrt-undiv_binary64_1135 flip-+_binary64_1075 unswap-sqr_binary64_1069 associate-*l/_binary64_1044
*-commutative_binary64_1032 frac-2neg_binary64_1112 clear-num_binary64_1100 associate-*r/_binary64_1043 pow-prod-down_binary64_1172 div-sub_binary64_1106
Counts
4 → 169
Calls

8 calls:

27.0ms
(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 -1 (sqrt.f64 (exp.f64 x)))))
11.0ms
(/.f64 (-.f64 1 (exp.f64 x)) (-.f64 -1 (sqrt.f64 (exp.f64 x))))
9.0ms
(-.f64 -1 (sqrt.f64 (exp.f64 x)))
4.0ms
(-.f64 1 (exp.f64 x))
0.0ms
(sqrt.f64 (exp.f64 x))

series155.0ms (0.3%)

Counts
4 → 24
Calls

4 calls:

72.0ms
(/.f64 (-.f64 1 (exp.f64 x)) (-.f64 -1 (sqrt.f64 (exp.f64 x))))
32.0ms
(-.f64 -1 (sqrt.f64 (exp.f64 x)))
30.0ms
(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 -1 (sqrt.f64 (exp.f64 x)))))
21.0ms
(-.f64 1 (exp.f64 x))
Compiler

Compiled 518 to 406 computations (21.6% saved)

simplify73.0ms (0.1%)

Algorithm
egg-herbie
Counts
193 → 193
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
050414440

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
0.0b
(+.f64 1 (sqrt.f64 (exp.f64 x)))
0.0b
(sqrt.f64 (exp.f64 x))
0.0b
(sqrt.f64 (exp.f64 x))
0.0b
(*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x)))) 2))
0.1b
(cbrt.f64 (*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x)))) 2)))
5.2b
(-.f64 (exp.f64 x) 1)
5.3b
(+.f64 -1 (sqrt.f64 (exp.f64 x)))

rewrite36.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt_binary64_1123
15×*-un-lft-identity_binary64_1101
12×add-exp-log_binary64_1139
add-log-exp_binary64_1140
add-cube-cbrt_binary64_1136 associate-*l*_binary64_1042
add-cbrt-cube_binary64_1137 associate-*r*_binary64_1041
prod-exp_binary64_1150
difference-of-squares_binary64_1070 pow1_binary64_1162 associate-*l/_binary64_1044
flip--_binary64_1076 flip3--_binary64_1105 unswap-sqr_binary64_1069 cancel-sign-sub-inv_binary64_1067
pow-exp_binary64_1169 difference-of-sqr-1_binary64_1071 distribute-lft-out--_binary64_1053 sqr-pow_binary64_1073 unpow2_binary64_1166 cbrt-div_binary64_1133
diff-log_binary64_1193 *-commutative_binary64_1032 cbrt-unprod_binary64_1134 pow1/3_binary64_1183 unpow-prod-down_binary64_1180 distribute-lft-out_binary64_1052 sum-log_binary64_1192 sub-neg_binary64_1094 flip3-+_binary64_1104 +-commutative_binary64_1031 flip-+_binary64_1075 pow-to-exp_binary64_1170 cbrt-prod_binary64_1132
Counts
4 → 72
Calls

8 calls:

12.0ms
(*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x)))) 2))
7.0ms
(cbrt.f64 (*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x)))) 2)))
4.0ms
(-.f64 (exp.f64 x) 1)
4.0ms
(+.f64 -1 (sqrt.f64 (exp.f64 x)))
0.0ms
(sqrt.f64 (exp.f64 x))

series557.0ms (1%)

Counts
4 → 24
Calls

4 calls:

378.0ms
(cbrt.f64 (*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x)))) 2)))
126.0ms
(*.f64 (-.f64 (exp.f64 x) 1) (pow.f64 (*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x)))) 2))
30.0ms
(+.f64 -1 (sqrt.f64 (exp.f64 x)))
23.0ms
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 646 to 496 computations (23.2% saved)

simplify60.0ms (0.1%)

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
058081184

prune18.9s (34%)

Pruning

429 alts after pruning (415 fresh and 14 done)

PrunedKeptTotal
New323163486
Fresh18252270
Picked000
Done01414
Total341429770
Error
0.0b
Counts
770 → 429
Compiler

Compiled 7976 to 4888 computations (38.7% saved)

simplify415.0ms (0.7%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
0496825576
1496825576

regimes2.7s (4.9%)

Compiler

Compiled 29963 to 22556 computations (24.7% saved)

bsearch0.0ms (0%)

regimes885.0ms (1.6%)

Compiler

Compiled 10310 to 8120 computations (21.2% saved)

bsearch0.0ms (0%)

regimes404.0ms (0.7%)

Compiler

Compiled 4473 to 3482 computations (22.2% saved)

bsearch0.0ms (0%)

regimes366.0ms (0.7%)

Compiler

Compiled 3987 to 3110 computations (22% saved)

bsearch0.0ms (0%)

regimes352.0ms (0.6%)

Compiler

Compiled 3847 to 2998 computations (22.1% saved)

bsearch0.0ms (0%)

regimes99.0ms (0.2%)

Compiler

Compiled 965 to 732 computations (24.1% saved)

bsearch0.0ms (0%)

regimes22.0ms (0%)

Compiler

Compiled 65 to 52 computations (20% saved)

bsearch0.0ms (0%)

regimes15.0ms (0%)

Compiler

Compiled 30 to 27 computations (10% saved)

bsearch0.0ms (0%)

regimes12.0ms (0%)

Accuracy

Total 0.3b remaining (98.5%)

Threshold costs 0.3b (98.5%)

Compiler

Compiled 16 to 17 computations (-6.3% saved)

bsearch11.0ms (0%)

Compiler

Compiled 195 to 153 computations (21.5% saved)

simplify7.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0221293
1221293

end0.0ms (0%)

sample13.3s (23.9%)

Algorithm
intervals
Results
502.0ms3958×body1024valid
132.0ms2011×body512valid
93.0ms8000×pre128true
61.0ms451×body2048valid
40.0ms1010×body256valid
12.0ms570×body128valid
Compiler

Compiled 13238 to 10049 computations (24.1% saved)

Pareto

0.9733755826243063

Profiling

Loading profile data...