Details

analyze69.0ms (2.3%)

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	50%	6.3%	6
43.7%	43.7%	12.6%	7
59.3%	26.5%	14.1%	8
59.3%	22.6%	18%	9
67.1%	13.7%	19.2%	10
67.1%	11.5%	21.4%	11
71%	6.9%	22%	12
71%	5.8%	23.2%	13
73%	3.5%	23.5%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample13.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	128	valid
0.0ms	11×	body	128	nan

Compiler

Compiled 13 to 13 computations (0% saved)

simplify100.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

20.3b

Counts

2 → 1

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

18.9b	(sqrt.f64 (+.f64 (*.f64 x x) y))
0.0b	(+.f64 (*.f64 x x) y)
0.0b	(+.f64 (*.f64 x x) y)
18.9b	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64_14780` `add-sqr-sqrt_binary64_14763`
3×	`*-un-lft-identity_binary64_14741` `sqrt-prod_binary64_14757` `pow1_binary64_14802` `add-cube-cbrt_binary64_14776`
2×	`add-exp-log_binary64_14779` `add-cbrt-cube_binary64_14777` `flip-+_binary64_14715` `flip3-+_binary64_14744` `sqrt-div_binary64_14758`
1×	`rem-sqrt-square_binary64_14754` `+-commutative_binary64_14671` `pow1/2_binary64_14821` `sqrt-pow1_binary64_14759` `sum-log_binary64_14832`

Counts

2 → 26

Calls

4 calls:

5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
4.0ms	(+.f64 (*.f64 x x) y)
0.0ms	(+.f64 (*.f64 x x) y)
0.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))

series125.0ms (4.1%)

Counts

2 → 26

Calls

2 calls:

69.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
56.0ms	(+.f64 (*.f64 x x) y)

Compiler

Compiled 322 to 299 computations (7.1% saved)

simplify37.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4963	546
1	4963	546

prune35.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	4	53

Error

0.0b

Counts

53 → 4

Compiler

Compiled 507 to 173 computations (65.9% saved)

localize10.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) y)) (cbrt.f64 (+.f64 (.f64 x x) y))) (cbrt.f64 (+.f64 (*.f64 x x) y)))
0.0b	(+.f64 (*.f64 x x) y)
0.0b	(+.f64 (*.f64 x x) y)
0.0b	(+.f64 (*.f64 x x) y)
18.9b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) y)) (cbrt.f64 (+.f64 (.f64 x x) y))) (cbrt.f64 (+.f64 (*.f64 x x) y))))
19.7b	(cbrt.f64 (+.f64 (*.f64 x x) y))
19.7b	(cbrt.f64 (+.f64 (*.f64 x x) y))
19.7b	(cbrt.f64 (+.f64 (*.f64 x x) y))

rewrite46.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`cbrt-div_binary64_14773`
30×	`flip-+_binary64_14715` `flip3-+_binary64_14744`
28×	`frac-times_binary64_14751`
26×	`sqrt-div_binary64_14758`
24×	`pow1_binary64_14802`
15×	`sqrt-pow1_binary64_14759`
14×	`associate-*l/_binary64_14684`
12×	`pow1/3_binary64_14823`
9×	`cbrt-prod_binary64_14772` `pow-prod-up_binary64_14811`
8×	`associate-*r/_binary64_14683`
7×	`add-sqr-sqrt_binary64_14763` `*-un-lft-identity_binary64_14741` `add-cube-cbrt_binary64_14776`
6×	`pow-plus_binary64_14804`
5×	`pow-prod-down_binary64_14812`
4×	`add-log-exp_binary64_14780` `add-exp-log_binary64_14779` `add-cbrt-cube_binary64_14777`
3×	`pow-sqr_binary64_14714`
2×	`pow2_binary64_14822`
1×	`pow3_binary64_14824` `pow1/2_binary64_14821` `sqrt-prod_binary64_14757`

Counts

4 → 89

Calls

8 calls:

20.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) y)) (cbrt.f64 (+.f64 (.f64 x x) y))) (cbrt.f64 (+.f64 (*.f64 x x) y))))
6.0ms	(cbrt.f64 (+.f64 (*.f64 x x) y))
4.0ms	(cbrt.f64 (+.f64 (*.f64 x x) y))
4.0ms	(cbrt.f64 (+.f64 (*.f64 x x) y))
0.0ms	(+.f64 (*.f64 x x) y)

series446.0ms (14.8%)

Counts

4 → 47

Calls

4 calls:

128.0ms	(cbrt.f64 (+.f64 (*.f64 x x) y))
123.0ms	(cbrt.f64 (+.f64 (*.f64 x x) y))
117.0ms	(cbrt.f64 (+.f64 (*.f64 x x) y))
78.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) y)) (cbrt.f64 (+.f64 (.f64 x x) y))) (cbrt.f64 (+.f64 (*.f64 x x) y))))

Compiler

Compiled 1897 to 1361 computations (28.3% saved)

simplify124.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4891	2969
1	4891	2969

prune124.0ms (4.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	136	4	140

Error

0.0b

Counts

140 → 4

Compiler

Compiled 3385 to 975 computations (71.2% saved)

localize5.0ms (0.2%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.0b

Counts

4 → 4

Compiler

Compiled 15 to 11 computations (26.7% saved)

localize10.0ms (0.3%)

Local error

Found 6 expressions with local error:

8.3b	(/.f64 (.f64 y 1/8) (.f64 x x))
0.0b	(.f64 (/.f64 y x) (-.f64 1/2 (/.f64 (.f64 y 1/8) (*.f64 x x))))
0.0b	(-.f64 1/2 (/.f64 (.f64 y 1/8) (.f64 x x)))
0.0b	(-.f64 1/2 (/.f64 (.f64 y 1/8) (.f64 x x)))
0.0b	(.f64 (/.f64 y x) (-.f64 1/2 (/.f64 (.f64 y 1/8) (*.f64 x x))))
8.3b	(/.f64 (.f64 y 1/8) (.f64 x x))

rewrite32.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_14763`
20×	`add-exp-log_binary64_14779` `add-cbrt-cube_binary64_14777`
18×	`*-un-lft-identity_binary64_14741`
15×	`cancel-sign-sub-inv_binary64_14707`
14×	`times-frac_binary64_14747` `add-cube-cbrt_binary64_14776`
13×	`associate-l_binary64_14682`
6×	`cbrt-unprod_binary64_14774` `distribute-lft-in_binary64_14690` `prod-exp_binary64_14790` `distribute-rgt-in_binary64_14691`
5×	`div-inv_binary64_14738` `cbrt-undiv_binary64_14775` `add-log-exp_binary64_14780` `div-exp_binary64_14792` `associate-r_binary64_14681` `pow1_binary64_14802`
3×	`sub-neg_binary64_14734` `flip--_binary64_14716` `flip3--_binary64_14745`
2×	`unswap-sqr_binary64_14709` `distribute-lft-out--_binary64_14693` `frac-times_binary64_14751` `associate-*r/_binary64_14683` `difference-of-squares_binary64_14710`
1×	`associate-/r_binary64_14685` `frac-2neg_binary64_14752` `pow-prod-down_binary64_14812` `diff-log_binary64_14833` `associate-/l_binary64_14686` `associate-l/_binary64_14684` `-commutative_binary64_14672` `clear-num_binary64_14740`

Counts

3 → 89

Calls

6 calls:

12.0ms	(.f64 (/.f64 y x) (-.f64 1/2 (/.f64 (.f64 y 1/8) (*.f64 x x))))
6.0ms	(/.f64 (.f64 y 1/8) (.f64 x x))
6.0ms	(-.f64 1/2 (/.f64 (.f64 y 1/8) (.f64 x x)))
0.0ms	(-.f64 1/2 (/.f64 (.f64 y 1/8) (.f64 x x)))
0.0ms	(.f64 (/.f64 y x) (-.f64 1/2 (/.f64 (.f64 y 1/8) (*.f64 x x))))

series416.0ms (13.8%)

Counts

3 → 30

Calls

3 calls:

219.0ms	(.f64 (/.f64 y x) (-.f64 1/2 (/.f64 (.f64 y 1/8) (*.f64 x x))))
112.0ms	(-.f64 1/2 (/.f64 (.f64 y 1/8) (.f64 x x)))
85.0ms	(/.f64 (.f64 y 1/8) (.f64 x x))

Compiler

Compiled 678 to 552 computations (18.6% saved)

simplify73.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4975	2024
1	4975	2024

prune101.0ms (3.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	119	4	123

Error

0.0b

Counts

123 → 4

Compiler

Compiled 2234 to 1138 computations (49.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	91
1	68	91

regimes116.0ms (3.9%)

Compiler: Compiled 240 to 204 computations (15% saved)

bsearch26.0ms (0.9%)

Steps

Iters	Range		Point
7	2.0107352593196325e+110	3.7184339992157633e+111	3.678899280452693e+111
9	-3.941421055227814e+154	-1.4017346459640663e+148	-1.3326463043900548e+154

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes89.0ms (2.9%)

Compiler: Compiled 78 to 88 computations (-12.8% saved)

bsearch25.0ms (0.8%)

Steps

Iters	Range		Point
8	3.3758758293800075e-71	1.4372033964571658e-68	1.4214720120609523e-68
4	-1.0326299125719494e-52	-7.112641376965221e-53	-8.017239489164489e-53

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes75.0ms (2.5%)

Compiler: Compiled 74 to 82 computations (-10.8% saved)

bsearch24.0ms (0.8%)

Steps

Iters	Range		Point
9	-2.2363250688100914e-292	-7.806397142385754e-299	-7.906639555763651e-299

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes66.0ms (2.2%)

Compiler: Compiled 30 to 48 computations (-60% saved)

bsearch22.0ms (0.7%)

Steps

Iters	Range		Point
9	1.40503500983695e-228	3.173344482254592e-220	1.8252824952360654e-221

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes63.0ms (2.1%)

Compiler: Compiled 16 to 36 computations (-125% saved)

bsearch16.0ms (0.5%)

Steps

Iters	Range		Point
8	-2.976888652806526e-307	9.088672529363319e-306	-4.12932189051984e-310

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes24.0ms (0.8%)

Compiler: Compiled 12 to 30 computations (-150% saved)

bsearch15.0ms (0.5%)

Steps

Iters	Range		Point
7	8.364975297770092e-141	8.31334556474453e-139	3.0155096972599033e-140

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes15.0ms (0.5%)

Accuracy

Total 0.1b remaining (98.4%)

Threshold costs 0.1b (98.4%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch5.0ms (0.2%)

Compiler: Compiled 86 to 65 computations (24.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	124
1	54	124

end0.0ms (0%)

sample632.0ms (21%)

Algorithm

1×

intervals

Results

202.0ms	8000×	body	128	valid
4.0ms	173×	body	128	nan

Compiler

Compiled 186 to 145 computations (22% saved)

Pareto

0.4862162106809245

Details

analyze69.0ms (2.3%)

sample13.0ms (0.4%)

simplify100.0ms (3.3%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite11.0ms (0.4%)

series125.0ms (4.1%)

simplify37.0ms (1.2%)

prune35.0ms (1.2%)

localize10.0ms (0.3%)

rewrite46.0ms (1.5%)

series446.0ms (14.8%)

simplify124.0ms (4.1%)

prune124.0ms (4.1%)

localize5.0ms (0.2%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.2%)

prune2.0ms (0.1%)

localize10.0ms (0.3%)

rewrite32.0ms (1.1%)

series416.0ms (13.8%)

simplify73.0ms (2.4%)

prune101.0ms (3.3%)

simplify4.0ms (0.1%)

regimes116.0ms (3.9%)

bsearch26.0ms (0.9%)

regimes89.0ms (2.9%)

bsearch25.0ms (0.8%)

regimes75.0ms (2.5%)

bsearch24.0ms (0.8%)

regimes66.0ms (2.2%)

bsearch22.0ms (0.7%)

regimes63.0ms (2.1%)

bsearch16.0ms (0.5%)

regimes24.0ms (0.8%)

bsearch15.0ms (0.5%)

regimes15.0ms (0.5%)

bsearch5.0ms (0.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample632.0ms (21%)

Profiling