Details

analyze1.0s (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
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)

sample37.0ms (0.1%)

Algorithm

1×

intervals

Results

24.0ms

256×

body

128

valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify138.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5236	55

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

29.7b

Counts

2 → 1

Compiler

Compiled 74 to 58 computations (21.6% saved)

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y)
0.0b	(+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)
0.0b	(+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328)
0.0b	(+.f64 (.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888)
0.1b	(.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)
0.1b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
0.1b	(.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
28.7b	(/.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))

rewrite75.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_12376`
15×	`add-cbrt-cube_binary64_12390` `add-exp-log_binary64_12392`
12×	`*-un-lft-identity_binary64_12354` `add-cube-cbrt_binary64_12389`
10×	`pow1_binary64_12415`
9×	`associate-l_binary64_12295` `associate-r_binary64_12294`
8×	`associate-/l/_binary64_12301` `associate-*l/_binary64_12297`
7×	`flip-+_binary64_12328` `flip3-+_binary64_12357`
4×	`frac-times_binary64_12364` `cbrt-unprod_binary64_12387` `add-log-exp_binary64_12393` `prod-exp_binary64_12403`
3×	`pow-prod-down_binary64_12425` `flip--_binary64_12329` `associate-/r_binary64_12298` `flip3--_binary64_12358` `times-frac_binary64_12360` `unswap-sqr_binary64_12322` `-commutative_binary64_12285`
2×	`cbrt-undiv_binary64_12388` `associate-/r/_binary64_12300` `associate-*r/_binary64_12296` `div-exp_binary64_12405`
1×	`clear-num_binary64_12353` `associate-/l*_binary64_12299` `div-inv_binary64_12351` `frac-2neg_binary64_12365`

Counts

4 → 91

Calls

8 calls:

34.0ms	(/.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))
11.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
10.0ms	(.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)
7.0ms	(.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
0.0ms	(+.f64 (.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888)

series1.6s (2.6%)

Counts

4 → 48

Calls

4 calls:

1.4s	(/.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))
109.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
88.0ms	(.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)
54.0ms	(.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)

Compiler

Compiled 4267 to 3504 computations (17.9% saved)

simplify113.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4996	5258
1	4996	5258

prune688.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	131	8	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	8	140

Error

0.0b

Counts

140 → 8

Compiler

Compiled 7270 to 5190 computations (28.6% saved)

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)
0.0b	(+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)
0.0b	(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)
0.0b	(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)
0.1b	(.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))
0.1b	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
0.1b	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
26.8b	(/.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))

rewrite74.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_12376`
18×	`*-un-lft-identity_binary64_12354` `add-cube-cbrt_binary64_12389`
12×	`add-cbrt-cube_binary64_12390` `add-exp-log_binary64_12392`
10×	`pow1_binary64_12415`
9×	`associate-l_binary64_12295` `associate-r_binary64_12294` `times-frac_binary64_12360`
6×	`associate-*r/_binary64_12296`
5×	`flip-+_binary64_12328` `flip3-+_binary64_12357`
4×	`add-log-exp_binary64_12393`
3×	`pow-prod-down_binary64_12425` `associate-/r_binary64_12298` `cbrt-unprod_binary64_12387` `associate-/l_binary64_12299` `prod-exp_binary64_12403` `distribute-lft-in_binary64_12303` `distribute-rgt-in_binary64_12304` `unswap-sqr_binary64_12322` `*-commutative_binary64_12285`
2×	`associate-/l/_binary64_12301` `associate-/r/_binary64_12300`
1×	`clear-num_binary64_12353` `div-inv_binary64_12351` `frac-2neg_binary64_12365` `cbrt-undiv_binary64_12388` `div-exp_binary64_12405`

Counts

4 → 97

Calls

8 calls:

28.0ms	(/.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))
14.0ms	(.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))
11.0ms	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
7.0ms	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))
0.0ms	(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)

series1.4s (2.2%)

Counts

4 → 48

Calls

4 calls:

1.1s	(/.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))
105.0ms	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104))
89.0ms	(.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104))
52.0ms	(.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))

Compiler

Compiled 3347 to 2766 computations (17.4% saved)

simplify96.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5457	5028

prune364.0ms (0.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	144	9	153

Error

0.0b

Counts

153 → 9

Compiler

Compiled 7403 to 5289 computations (28.6% saved)

localize43.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)
0.0b	(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)
0.0b	(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)
0.0b	(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)
0.3b	(cbrt.f64 (/.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)))
26.8b	(/.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))
26.8b	(/.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))
26.8b	(/.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))

rewrite152.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64_12360`
35×	`*-un-lft-identity_binary64_12354` `add-sqr-sqrt_binary64_12376` `add-cube-cbrt_binary64_12389`
15×	`cbrt-prod_binary64_12385`
10×	`add-cbrt-cube_binary64_12390` `add-exp-log_binary64_12392`
9×	`associate-/r_binary64_12298` `associate-/l_binary64_12299`
8×	`associate-/r/_binary64_12300`
7×	`flip-+_binary64_12328` `flip3-+_binary64_12357`
6×	`associate-/l/_binary64_12301`
4×	`div-inv_binary64_12351` `add-log-exp_binary64_12393` `pow1_binary64_12415`
3×	`clear-num_binary64_12353` `frac-2neg_binary64_12365` `cbrt-undiv_binary64_12388` `div-exp_binary64_12405`
1×	`cbrt-div_binary64_12386` `pow1/3_binary64_12436`

Counts

4 → 117

Calls

8 calls:

32.0ms	(/.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))
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))
29.0ms	(/.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))
25.0ms	(cbrt.f64 (/.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)))
0.0ms	(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)

series40.7s (65.4%)

Counts

4 → 96

Calls

4 calls:

37.2s	(cbrt.f64 (/.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)))
1.2s	(/.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))
1.2s	(/.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))
1.2s	(/.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))

Compiler

Compiled 36098 to 29009 computations (19.6% saved)

simplify345.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5675	33727

prune3.8s (6.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	213	9	222

Error

0.0b

Counts

222 → 9

Compiler

Compiled 39808 to 28564 computations (28.2% saved)

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)
0.0b	(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)
0.0b	(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)
0.0b	(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)
7.9b	(sqrt.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
16.6b	(/.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)))
16.8b	(.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 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (sqrt.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))))
23.4b	(/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (sqrt.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)))

rewrite179.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

126×	`add-sqr-sqrt_binary64_12376`
108×	`times-frac_binary64_12360`
95×	`*-un-lft-identity_binary64_12354`
69×	`add-cube-cbrt_binary64_12389`
63×	`sqrt-prod_binary64_12370`
36×	`associate-l_binary64_12295`
24×	`associate-r_binary64_12294`
20×	`add-cbrt-cube_binary64_12390` `add-exp-log_binary64_12392`
13×	`distribute-lft-out--_binary64_12306` `difference-of-squares_binary64_12323`
12×	`associate-/r*_binary64_12298`
10×	`sqrt-div_binary64_12371`
9×	`unswap-sqr_binary64_12322`
8×	`associate-/l*_binary64_12299` `associate-/r/_binary64_12300`
7×	`pow1_binary64_12415`
6×	`cbrt-undiv_binary64_12388` `flip-+_binary64_12328` `div-exp_binary64_12405` `flip3-+_binary64_12357`
4×	`cbrt-unprod_binary64_12387` `div-inv_binary64_12351` `associate-/l/_binary64_12301` `add-log-exp_binary64_12393` `prod-exp_binary64_12403`
2×	`clear-num_binary64_12353` `frac-2neg_binary64_12365`
1×	`pow-prod-down_binary64_12425` `flip--_binary64_12329` `frac-times_binary64_12364` `div-sub_binary64_12359` `sqrt-pow1_binary64_12372` `pow1/2_binary64_12434` `rem-sqrt-square_binary64_12367` `associate-l/_binary64_12297` `associate-r/_binary64_12296` `flip3--_binary64_12358` `*-commutative_binary64_12285`

Counts

4 → 205

Calls

8 calls:

65.0ms	(.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 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (sqrt.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))))
29.0ms	(/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (sqrt.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)))
18.0ms	(/.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 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))
0.0ms	(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)

series2.7s (4.3%)

Counts

4 → 68

Calls

4 calls:

1.4s	(.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 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (sqrt.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))))
1.2s	(/.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)) 604816789577447/4398046511104)) y)) z) (sqrt.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328)))
77.0ms	(/.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)))
71.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (*.f64 x (+.f64 x 6099563062176297/140737488355328)) 1158907574534893/4398046511104)) 172293041005667/549755813888)) 6624073998258585/140737488355328))

Compiler

Compiled 7136 to 5926 computations (17% saved)

simplify227.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5666	18888

prune1.6s (2.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	272	1	273
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	272	10	282

Error

0.0b

Counts

282 → 10

Compiler

Compiled 19952 to 14602 computations (26.8% saved)

simplify53.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	829	3136
1	829	3136

regimes796.0ms (1.3%)

Compiler: Compiled 6306 to 4863 computations (22.9% saved)

bsearch128.0ms (0.2%)

Steps

Iters	Range		Point
11	1.4465903595282533e+35	1.5392582005786722e+58	6.795307804012348e+46
8	-3.6142788988219845e+39	-8.936985559543527e+36	-1.6281278315350795e+39

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes756.0ms (1.2%)

Compiler: Compiled 5763 to 4455 computations (22.7% saved)

bsearch78.0ms (0.1%)

Steps

Iters	Range		Point
11	1.4465903595282533e+35	1.5392582005786722e+58	1.379915533616411e+52
8	-3.6142788988219845e+39	-8.936985559543527e+36	-2.5935894075575574e+39

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes257.0ms (0.4%)

Compiler: Compiled 645 to 564 computations (12.6% saved)

bsearch87.0ms (0.1%)

Steps

Iters	Range		Point
11	1.4465903595282533e+35	1.5392582005786722e+58	2.25550138098064e+35
11	-5.179590027883701e+31	-0.36545130870857273	-1.127219345480494e+16

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes243.0ms (0.4%)

Compiler: Compiled 546 to 486 computations (11% saved)

bsearch79.0ms (0.1%)

Steps

Iters	Range		Point
9	567080269557710.6	5.746500182648009e+23	1.4246719417432672e+17
11	-5.179590027883701e+31	-0.36545130870857273	-12335511.506067034

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes234.0ms (0.4%)

Compiler: Compiled 447 to 408 computations (8.7% saved)

bsearch75.0ms (0.1%)

Steps

Iters	Range		Point
11	1.4465903595282533e+35	1.5392582005786722e+58	1.4621033240230302e+35
8	-3.6142788988219845e+39	-8.936985559543527e+36	-9.026779232908714e+36

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes208.0ms (0.3%)

Compiler: Compiled 273 to 270 computations (1.1% saved)

bsearch77.0ms (0.1%)

Steps

Iters	Range		Point
11	1.0101183495137219e-10	1066048663568.6902	1.9960170958710715
8	-0.34239099771653353	-0.0010108774513707137	-0.17614395995223925

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes178.0ms (0.3%)

Compiler: Compiled 186 to 207 computations (-11.3% saved)

bsearch69.0ms (0.1%)

Steps

Iters	Range		Point
11	1.0101183495137219e-10	1066048663568.6902	0.4270998902787421
8	-0.34239099771653353	-0.0010108774513707137	-0.20056122210261773

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes149.0ms (0.2%)

Compiler: Compiled 123 to 159 computations (-29.3% saved)

bsearch41.0ms (0.1%)

Steps

Iters	Range		Point
4	274996758701967.22	496212802214177.8	278554481538231.25
8	-0.34239099771653353	-0.0010108774513707137	-0.23311757163645572

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes146.0ms (0.2%)

Compiler: Compiled 72 to 117 computations (-62.5% saved)

bsearch63.0ms (0.1%)

Steps

Iters	Range		Point
11	1.0101183495137219e-10	1066048663568.6902	21.695285600705567
8	-0.34239099771653353	-0.0010108774513707137	-0.17614395995223925

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes120.0ms (0.2%)

Compiler: Compiled 33 to 84 computations (-154.5% saved)

bsearch60.0ms (0.1%)

Steps

Iters	Range		Point
11	1.0101183495137219e-10	1066048663568.6902	1.9960170958710715
8	-0.34239099771653353	-0.0010108774513707137	-0.2650696675736684

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes31.0ms (0%)

Compiler: Compiled 24 to 69 computations (-187.5% saved)

bsearch0.0ms (0%)

regimes28.0ms (0%)

Accuracy

Total 0.8b remaining (98.9%)

Threshold costs 0.8b (98.9%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch28.0ms (0%)

Compiler: Compiled 788 to 552 computations (29.9% saved)

simplify24.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	510	957
1	510	957

end0.0ms (0%)

sample2.8s (4.5%)

Algorithm

1×

intervals

Results

708.0ms	8000×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 2855 to 2177 computations (23.7% saved)

Pareto

0.9849987664181815

Details

analyze1.0s (1.7%)

sample37.0ms (0.1%)

simplify138.0ms (0.2%)

prune4.0ms (0%)

localize30.0ms (0%)

rewrite75.0ms (0.1%)

series1.6s (2.6%)

simplify113.0ms (0.2%)

prune688.0ms (1.1%)

localize25.0ms (0%)

rewrite74.0ms (0.1%)

series1.4s (2.2%)

simplify96.0ms (0.2%)

prune364.0ms (0.6%)

localize43.0ms (0.1%)

rewrite152.0ms (0.2%)

series40.7s (65.4%)

simplify345.0ms (0.6%)

prune3.8s (6.1%)

localize30.0ms (0%)

rewrite179.0ms (0.3%)

series2.7s (4.3%)

simplify227.0ms (0.4%)

prune1.6s (2.6%)

simplify53.0ms (0.1%)

regimes796.0ms (1.3%)

bsearch128.0ms (0.2%)

regimes756.0ms (1.2%)

bsearch78.0ms (0.1%)

regimes257.0ms (0.4%)

bsearch87.0ms (0.1%)

regimes243.0ms (0.4%)

bsearch79.0ms (0.1%)

regimes234.0ms (0.4%)

bsearch75.0ms (0.1%)

regimes208.0ms (0.3%)

bsearch77.0ms (0.1%)

regimes178.0ms (0.3%)

bsearch69.0ms (0.1%)

regimes149.0ms (0.2%)

bsearch41.0ms (0.1%)

regimes146.0ms (0.2%)

bsearch63.0ms (0.1%)

regimes120.0ms (0.2%)

bsearch60.0ms (0.1%)

regimes31.0ms (0%)

bsearch0.0ms (0%)

regimes28.0ms (0%)

bsearch28.0ms (0%)

simplify24.0ms (0%)

end0.0ms (0%)

sample2.8s (4.5%)

Profiling