Details

Time bar (total: 4.9s)

analyze958.0ms (19.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%74.9%0.1%6
25%74.9%0.1%7
37.4%62.4%0.1%8
37.4%62.4%0.1%9
37.4%62.4%0.1%10
43.7%56.2%0.1%11
43.7%56.2%0.1%12
43.7%56.2%0.1%13
61.7%38.2%0.1%14
Compiler

Compiled 38 to 30 computations (21.1% saved)

sample29.0ms (0.6%)

Algorithm
intervals
Results
20.0ms256×body80valid
Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify32.0ms (0.7%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0512255

prune9.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 25.5b

Counts
2 → 1
Compiler

Compiled 74 to 58 computations (21.6% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x)
0.0b
(*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)
0.1b
(*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
24.7b
(/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))

rewrite72.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
15×add-exp-log_binary64 add-cbrt-cube_binary64
12×*-un-lft-identity_binary64 add-cube-cbrt_binary64
10×pow1_binary64
associate-*r*_binary64 associate-*l*_binary64
associate-/l/_binary64 associate-*l/_binary64
flip3-+_binary64 flip-+_binary64
add-log-exp_binary64 cbrt-unprod_binary64 prod-exp_binary64 frac-times_binary64
pow-prod-down_binary64 associate-/r*_binary64 flip3--_binary64 unswap-sqr_binary64 times-frac_binary64 flip--_binary64 *-commutative_binary64
cbrt-undiv_binary64 associate-*r/_binary64 associate-/r/_binary64 div-exp_binary64
clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64
Counts
4 → 91
Calls

4 calls:

35.0ms
(/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))
15.0ms
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x)
10.0ms
(*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)
8.0ms
(*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)

series64.0ms (1.3%)

Counts
4 → 12
Calls

4 calls:

44.0ms
(/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))
9.0ms
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x)
6.0ms
(*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
4.0ms
(*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)

simplify124.0ms (2.5%)

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (82.0ms)

IterNodesCost
049473198
149473198

prune213.0ms (4.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New967103
Fresh000
Picked101
Done000
Total977104

Merged error: 0.0b

Counts
104 → 7
Compiler

Compiled 5185 to 3694 computations (28.8% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y))
0.0b
(*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))
0.1b
(*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
24.1b
(/.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))

rewrite65.0ms (1.3%)

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt_binary64
18×*-un-lft-identity_binary64 add-cube-cbrt_binary64
12×add-exp-log_binary64 add-cbrt-cube_binary64
10×pow1_binary64
associate-*r*_binary64 associate-*l*_binary64 times-frac_binary64
associate-*r/_binary64
flip3-+_binary64 flip-+_binary64
add-log-exp_binary64
pow-prod-down_binary64 associate-/r*_binary64 cbrt-unprod_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 prod-exp_binary64 associate-/l*_binary64 *-commutative_binary64
associate-/l/_binary64 associate-/r/_binary64
cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64
Counts
4 → 97
Calls

4 calls:

30.0ms
(/.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
15.0ms
(*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y))
10.0ms
(*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))
7.0ms
(*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))

series63.0ms (1.3%)

Counts
4 → 12
Calls

4 calls:

43.0ms
(/.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
9.0ms
(*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y))
6.0ms
(*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
4.0ms
(*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))

simplify119.0ms (2.4%)

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 0 (78.0ms)

IterNodesCost
049663537
149663537

prune200.0ms (4.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1090109
Fresh066
Picked011
Done000
Total1097116

Merged error: 0.0b

Counts
116 → 7
Compiler

Compiled 5512 to 3934 computations (28.6% saved)

localize33.0ms (0.7%)

Local error

Found 4 expressions with local error:

8.4b
(sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
8.4b
(sqrt.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))
14.1b
(/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)))
21.0b
(/.f64 (*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))) (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z)) (sqrt.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328)))

rewrite105.0ms (2.1%)

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt_binary64
43×*-un-lft-identity_binary64
36×times-frac_binary64
30×sqrt-prod_binary64
29×add-cube-cbrt_binary64
15×add-exp-log_binary64 add-cbrt-cube_binary64
12×associate-/r*_binary64
sqrt-div_binary64
associate-/l/_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
flip3-+_binary64 pow1_binary64 associate-/l*_binary64 flip-+_binary64
cbrt-undiv_binary64 div-exp_binary64
add-log-exp_binary64 associate-/r/_binary64
pow1/2_binary64 cbrt-unprod_binary64 associate-*r/_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 div-inv_binary64 frac-times_binary64
flip3--_binary64 div-sub_binary64 flip--_binary64 associate-*l/_binary64
Counts
4 → 124
Calls

4 calls:

52.0ms
(/.f64 (*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))) (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z)) (sqrt.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328)))
21.0ms
(/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)))
13.0ms
(sqrt.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))
13.0ms
(sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))

series71.0ms (1.4%)

Counts
4 → 12
Calls

4 calls:

45.0ms
(/.f64 (*.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))) (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z)) (sqrt.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328)))
12.0ms
(/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)))
7.0ms
(sqrt.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
7.0ms
(sqrt.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))

simplify111.0ms (2.2%)

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
055456774

prune423.0ms (8.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1360136
Fresh055
Picked011
Done011
Total1367143

Merged error: 0.0b

Counts
143 → 7
Compiler

Compiled 9290 to 6841 computations (26.4% saved)

localize31.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x)
0.0b
(*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))
0.1b
(*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
25.1b
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 2 2)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (*.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328) (+.f64 x 2)))

rewrite79.0ms (1.6%)

Algorithm
rewrite-expression-head
Rules
22×add-exp-log_binary64 add-cbrt-cube_binary64
16×add-sqr-sqrt_binary64
12×flip3-+_binary64 flip-+_binary64
10×*-un-lft-identity_binary64 pow1_binary64 add-cube-cbrt_binary64
associate-*r*_binary64 associate-*l*_binary64
associate-/l/_binary64 associate-/r/_binary64 frac-times_binary64 associate-*l/_binary64
cbrt-unprod_binary64 prod-exp_binary64
associate-*r/_binary64
add-log-exp_binary64 cbrt-undiv_binary64 div-exp_binary64
pow-prod-down_binary64 flip3--_binary64 unswap-sqr_binary64 flip--_binary64 *-commutative_binary64
associate-/r*_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 times-frac_binary64 div-inv_binary64
Counts
4 → 99
Calls

4 calls:

42.0ms
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 2 2)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (*.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328) (+.f64 x 2)))
15.0ms
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x)
10.0ms
(*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))
8.0ms
(*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)

series75.0ms (1.5%)

Counts
4 → 12
Calls

4 calls:

55.0ms
(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 2 2)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (*.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328) (+.f64 x 2)))
9.0ms
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x)
7.0ms
(*.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
4.0ms
(*.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))

simplify96.0ms (1.9%)

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
051513832

prune219.0ms (4.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1101111
Fresh134
Picked101
Done022
Total1126118

Merged error: 0.0b

Counts
118 → 6
Compiler

Compiled 6107 to 4234 computations (30.7% saved)

regimes220.0ms (4.5%)

Compiler

Compiled 888 to 690 computations (22.3% saved)

bsearch37.0ms (0.8%)

Steps
ItersRangePoint
10
1.2075886598982471e+37
3.971447035505544e+48
3.698678048591889e+48
5
-2.3074284506636555e+28
-1.1036901078926954e+28
-2.2749166960115483e+28
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
08085
18085

end0.0ms (0%)

sample1.4s (29.1%)

Algorithm
intervals
Results
629.0ms8000×body80valid
1.0msbody80invalid
Compiler

Compiled 464 to 350 computations (24.6% saved)

Profiling

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