Details

analyze987.0ms (0.7%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
31.2%	68.7%	0.1%	5
31.2%	59.3%	9.5%	6
34.3%	54.6%	11%	7
34.3%	49.2%	16.5%	8
35.9%	46.4%	17.7%	9
35.9%	42.1%	22%	10
36.7%	40.6%	22.7%	11
36.7%	39.1%	24.2%	12
37.1%	38.3%	24.7%	13
37.1%	36.7%	26.2%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample414.0ms (0.3%)

Algorithm

1×

intervals

Results

252.0ms	129×	body	8192	exit
30.0ms	80×	body	1024	nan
18.0ms	256×	body	128	valid
9.0ms	49×	body	512	nan
3.0ms	23×	body	256	nan
2.0ms	1×	body	4096	nan
0.0ms	9×	body	128	nan
0.0ms	3×	body	128	overflowed
0.0ms	1×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify89.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

656×	`unswap-sqr_binary64`
607×	`times-frac_binary64`
540×	`sqr-pow_binary64`
391×	`pow-sqr_binary64`
205×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	37	11
3	79	11
4	200	11
5	635	11
6	2301	11
7	2298	11
8	2410	11
9	2637	11
10	3067	11
11	3698	11
12	4907	11
13	4890	11

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))

Compiler

Compiled 35 to 18 computations (48.6% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
✓	0.3b	(pow.f64 l (exp.f64 w))

series662.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

411.0ms	(pow.f64 l (exp.f64 w))
251.0ms	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
15×	`unpow-prod-down_binary64`

Counts

2 → 66

Calls

2 calls:

4.0ms	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
2.0ms	(pow.f64 l (exp.f64 w))

simplify91.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

847×	`fma-def_binary64`
696×	`associate-l_binary64`
359×	`fma-neg_binary64`
322×	`times-frac_binary64`
234×	`associate-/l*_binary64`

Counts

106 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	1790
1	375	1705
2	1326	1665
3	4894	1665
4	5116	1665

prune90.0ms (0.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	5	92

Error

0.1b

Counts

92 → 5

Alt Table

Status	Error	Program
	11.0b	(/.f64 (+.f64 l (+.f64 (.f64 1/6 (.f64 (log.f64 l) (.f64 l (pow.f64 w 3)))) (+.f64 (.f64 1/2 (.f64 (pow.f64 (log.f64 l) 2) (.f64 l (pow.f64 w 3)))) (+.f64 (.f64 1/2 (.f64 (log.f64 l) (.f64 l (pow.f64 w 2)))) (+.f64 (.f64 1/2 (.f64 (pow.f64 (log.f64 l) 2) (.f64 l (pow.f64 w 2)))) (+.f64 (.f64 (log.f64 l) (.f64 l w)) (.f64 1/6 (.f64 (pow.f64 (log.f64 l) 3) (*.f64 l (pow.f64 w 3)))))))))) (exp.f64 w))
	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 l (exp.f64 w))) (cbrt.f64 (pow.f64 l (exp.f64 w)))) (sqrt.f64 (exp.f64 w))) (/.f64 (cbrt.f64 (pow.f64 l (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
▶	0.7b	(/.f64 (pow.f64 (sqrt.f64 l) (exp.f64 w)) (/.f64 (exp.f64 w) (pow.f64 (sqrt.f64 l) (exp.f64 w))))
	14.8b	(-.f64 (fma.f64 1/6 (.f64 (.f64 l (pow.f64 w 3)) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 3))) (+.f64 (fma.f64 (log.f64 l) (.f64 l w) l) (.f64 (.f64 l (.f64 w w)) (+.f64 (.f64 1/2 (pow.f64 (log.f64 l) 2)) 1/2)))) (fma.f64 l (.f64 (pow.f64 w 3) 1/6) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (*.f64 w w))))))
	2.4b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))

Compiler

Compiled 1952 to 706 computations (63.8% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (exp.f64 w) (pow.f64 (sqrt.f64 l) (exp.f64 w)))
✓	0.2b	(pow.f64 (sqrt.f64 l) (exp.f64 w))
✓	0.2b	(/.f64 (pow.f64 (sqrt.f64 l) (exp.f64 w)) (/.f64 (exp.f64 w) (pow.f64 (sqrt.f64 l) (exp.f64 w))))

series747.0ms (0.5%)

Counts

3 → 28

Calls

3 calls:

340.0ms	(/.f64 (pow.f64 (sqrt.f64 l) (exp.f64 w)) (/.f64 (exp.f64 w) (pow.f64 (sqrt.f64 l) (exp.f64 w))))
245.0ms	(/.f64 (exp.f64 w) (pow.f64 (sqrt.f64 l) (exp.f64 w)))
161.0ms	(pow.f64 (sqrt.f64 l) (exp.f64 w))

rewrite114.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

700×	`times-frac_binary64`
438×	`unpow-prod-down_binary64`
354×	`*-un-lft-identity_binary64`
354×	`add-sqr-sqrt_binary64`
354×	`add-cube-cbrt_binary64`

Counts

3 → 495

Calls

3 calls:

14.0ms	(/.f64 (pow.f64 (sqrt.f64 l) (exp.f64 w)) (/.f64 (exp.f64 w) (pow.f64 (sqrt.f64 l) (exp.f64 w))))
6.0ms	(pow.f64 (sqrt.f64 l) (exp.f64 w))
5.0ms	(/.f64 (exp.f64 w) (pow.f64 (sqrt.f64 l) (exp.f64 w)))

simplify528.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

757×	`associate-/l*_binary64`
586×	`associate-/r/_binary64`
575×	`associate-/l/_binary64`
356×	`associate-*r/_binary64`
314×	`associate-*l/_binary64`

Counts

523 → 628

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	636	22645
1	1337	21193
2	4627	21136
3	4998	21136
4	5023	21136

prune688.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	658	3	661
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	660	6	666

Error

0.1b

Counts

666 → 6

Alt Table

Status	Error	Program
	2.1b	(/.f64 (pow.f64 (sqrt.f64 l) (exp.f64 w)) (expm1.f64 (log1p.f64 (/.f64 (exp.f64 w) (pow.f64 (sqrt.f64 l) (exp.f64 w))))))
	14.8b	(-.f64 (fma.f64 1/6 (.f64 (.f64 l (pow.f64 w 3)) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 3))) (+.f64 (fma.f64 (log.f64 l) (.f64 l w) l) (.f64 (.f64 l (.f64 w w)) (+.f64 (.f64 1/2 (pow.f64 (log.f64 l) 2)) 1/2)))) (fma.f64 l (.f64 (pow.f64 w 3) 1/6) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (*.f64 w w))))))
✓	0.7b	(/.f64 (pow.f64 (sqrt.f64 l) (exp.f64 w)) (/.f64 (exp.f64 w) (pow.f64 (sqrt.f64 l) (exp.f64 w))))
	1.8b	(.f64 (pow.f64 (.f64 (cbrt.f64 (sqrt.f64 l)) (cbrt.f64 (sqrt.f64 l))) (*.f64 2 (exp.f64 w))) (/.f64 (pow.f64 (cbrt.f64 (sqrt.f64 l)) (exp.f64 w)) (/.f64 (exp.f64 w) (pow.f64 (cbrt.f64 (sqrt.f64 l)) (exp.f64 w)))))
	2.4b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))
▶	0.6b	(/.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (/.f64 (exp.f64 w) (pow.f64 (sqrt.f64 l) (exp.f64 w))))

Compiler

Compiled 21302 to 3804 computations (82.1% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))
	0.2b	(/.f64 (exp.f64 w) (pow.f64 (sqrt.f64 l) (exp.f64 w)))
	0.2b	(pow.f64 (sqrt.f64 l) (exp.f64 w))
✓	0.2b	(/.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (/.f64 (exp.f64 w) (pow.f64 (sqrt.f64 l) (exp.f64 w))))

series1.1s (0.8%)

Counts

2 → 20

Calls

2 calls:

646.0ms

(/.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (/.f64 (exp.f64 w) (pow.f64 (sqrt.f64 l) (exp.f64 w))))

494.0ms

(pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))

rewrite170.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

926×	`times-frac_binary64`
846×	`unpow-prod-down_binary64`
447×	`*-un-lft-identity_binary64`
447×	`add-sqr-sqrt_binary64`
447×	`add-cube-cbrt_binary64`

Counts

2 → 590

Calls

2 calls:

19.0ms

(/.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (/.f64 (exp.f64 w) (pow.f64 (sqrt.f64 l) (exp.f64 w))))

4.0ms

(pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))

simplify791.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

829×	`associate-/l*_binary64`
734×	`associate-/r/_binary64`
466×	`associate-/l/_binary64`
441×	`associate-*l/_binary64`
161×	`fma-def_binary64`

Counts

610 → 777

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	804	36895
1	1573	33171
2	4828	32915
3	4993	32915
4	5013	32915

prune896.0ms (0.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	880	3	883
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	884	5	889

Error

0.0b

Counts

889 → 5

Alt Table

Status	Error	Program
▶	0.6b	(/.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (/.f64 (sqrt.f64 (exp.f64 w)) 1)) (/.f64 (sqrt.f64 (exp.f64 w)) (pow.f64 (sqrt.f64 l) (exp.f64 w))))
	0.7b	(/.f64 (sqrt.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))) (/.f64 (exp.f64 w) (*.f64 (sqrt.f64 (pow.f64 (sqrt.f64 l) (exp.f64 w))) (pow.f64 (sqrt.f64 l) (exp.f64 w)))))
	3.7b	(/.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (/.f64 (exp.f64 w) (exp.f64 (log.f64 (pow.f64 (sqrt.f64 l) (exp.f64 w))))))
	14.8b	(-.f64 (fma.f64 1/6 (.f64 (.f64 l (pow.f64 w 3)) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 3))) (+.f64 (fma.f64 (log.f64 l) (.f64 l w) l) (.f64 (.f64 l (.f64 w w)) (+.f64 (.f64 1/2 (pow.f64 (log.f64 l) 2)) 1/2)))) (fma.f64 l (.f64 (pow.f64 w 3) 1/6) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (*.f64 w w))))))
	2.4b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))

Compiler

Compiled 35580 to 5413 computations (84.8% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))
✓	0.2b	(/.f64 (sqrt.f64 (exp.f64 w)) (pow.f64 (sqrt.f64 l) (exp.f64 w)))
	0.2b	(pow.f64 (sqrt.f64 l) (exp.f64 w))
✓	0.2b	(/.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (/.f64 (sqrt.f64 (exp.f64 w)) 1)) (/.f64 (sqrt.f64 (exp.f64 w)) (pow.f64 (sqrt.f64 l) (exp.f64 w))))

series890.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

676.0ms

(/.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (/.f64 (sqrt.f64 (exp.f64 w)) 1)) (/.f64 (sqrt.f64 (exp.f64 w)) (pow.f64 (sqrt.f64 l) (exp.f64 w))))

214.0ms

(/.f64 (sqrt.f64 (exp.f64 w)) (pow.f64 (sqrt.f64 l) (exp.f64 w)))

rewrite12.0s (8%)

Algorithm

1×	rewrite-expression-head

Rules

75332×	`times-frac_binary64`
34226×	`unpow-prod-down_binary64`
29906×	`*-un-lft-identity_binary64`
29906×	`add-sqr-sqrt_binary64`
29906×	`add-cube-cbrt_binary64`

Counts

2 → 20585

Calls

2 calls:

425.0ms

(/.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (/.f64 (sqrt.f64 (exp.f64 w)) 1)) (/.f64 (sqrt.f64 (exp.f64 w)) (pow.f64 (sqrt.f64 l) (exp.f64 w))))

6.0ms

(/.f64 (sqrt.f64 (exp.f64 w)) (pow.f64 (sqrt.f64 l) (exp.f64 w)))

simplify39.8s (26.5%)

Algorithm

1×	egg-herbie

Counts

20609 → 13348

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5853	2077080

prune17.1s (11.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	13427	0	13427
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	13427	5	13432

Error

0.0b

Counts

13432 → 5

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (/.f64 (sqrt.f64 (exp.f64 w)) 1)) (/.f64 (sqrt.f64 (exp.f64 w)) (pow.f64 (sqrt.f64 l) (exp.f64 w))))
	0.7b	(/.f64 (sqrt.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))) (/.f64 (exp.f64 w) (*.f64 (sqrt.f64 (pow.f64 (sqrt.f64 l) (exp.f64 w))) (pow.f64 (sqrt.f64 l) (exp.f64 w)))))
	3.7b	(/.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (/.f64 (exp.f64 w) (exp.f64 (log.f64 (pow.f64 (sqrt.f64 l) (exp.f64 w))))))
	14.8b	(-.f64 (fma.f64 1/6 (.f64 (.f64 l (pow.f64 w 3)) (+.f64 (log.f64 l) (pow.f64 (log.f64 l) 3))) (+.f64 (fma.f64 (log.f64 l) (.f64 l w) l) (.f64 (.f64 l (.f64 w w)) (+.f64 (.f64 1/2 (pow.f64 (log.f64 l) 2)) 1/2)))) (fma.f64 l (.f64 (pow.f64 w 3) 1/6) (.f64 l (+.f64 w (.f64 (log.f64 (sqrt.f64 l)) (*.f64 w w))))))
	2.4b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))

Compiler

Compiled 841121 to 207380 computations (75.3% saved)

regimes20.0s (13.4%)

Accuracy

Total 0.2b remaining (67.3%)

Threshold costs 0.2b (67.3%)

Counts

3370 → 1

Compiler

Compiled 471413 to 216400 computations (54.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	8	20

end0.0ms (0%)

Compiler: Compiled 14 to 7 computations (50% saved)

sample52.7s (35.1%)

Algorithm

1×

intervals

Results

8.2s	4617×	body	8192	exit
1.1s	3210×	body	1024	nan
465.0ms	8000×	body	128	valid
293.0ms	1587×	body	512	nan
92.0ms	795×	body	256	nan
15.0ms	315×	body	128	nan
11.0ms	146×	body	128	overflowed
7.0ms	110×	body	128	invalid
4.0ms	3×	body	4096	nan
3.0ms	1×	body	8192	nan
1.0ms	1×	body	2048	nan

Compiler

Compiled 210 to 118 computations (43.8% saved)

Details

analyze987.0ms (0.7%)

sample414.0ms (0.3%)

simplify89.0ms (0.1%)

prune2.0ms (0%)

localize4.0ms (0%)

series662.0ms (0.4%)

rewrite9.0ms (0%)

simplify91.0ms (0.1%)

prune90.0ms (0.1%)

localize7.0ms (0%)

series747.0ms (0.5%)

rewrite114.0ms (0.1%)

simplify528.0ms (0.4%)

prune688.0ms (0.5%)

localize9.0ms (0%)

series1.1s (0.8%)

rewrite170.0ms (0.1%)

simplify791.0ms (0.5%)

prune896.0ms (0.6%)

localize12.0ms (0%)

series890.0ms (0.6%)

rewrite12.0s (8%)

simplify39.8s (26.5%)

prune17.1s (11.4%)

regimes20.0s (13.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample52.7s (35.1%)

Profiling