Details

analyze2.0s (6.2%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
3.1%	96.8%	0.1%	7
3.1%	96.8%	0.1%	8
4.7%	95.2%	0.1%	9
4.7%	93.9%	1.5%	10
5.4%	93.1%	1.6%	11
5.4%	93%	1.6%	12
5.8%	92.6%	1.6%	13
5.8%	91.8%	2.4%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample20.0s (60.4%)

Results

15.7s	11175×	body	8192	exit
2.0s	3239×	body	1024	invalid
1.3s	8256×	body	128	valid
622.0ms	1686×	body	512	invalid
199.0ms	813×	body	256	invalid
55.0ms	364×	body	128	invalid
9.0ms	3×	body	8192	invalid
6.0ms	6×	body	2048	invalid
2.0ms	1×	body	4096	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify90.0ms (0.3%)

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

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.3b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 55 to 32 computations (41.8% 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))

series304.0ms (0.9%)

Counts

2 → 40

Calls

2 calls:

156.0ms	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
148.0ms	(pow.f64 l (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))

simplify81.0ms (0.2%)

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

prune77.0ms (0.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	89	4	93

Error

0.0b

Counts

93 → 4

Alt Table

Status	Error	Program
	4.7b	(/.f64 (exp.f64 (*.f64 (log.f64 l) (exp.f64 w))) (exp.f64 w))
▶	0.3b	(/.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (exp.f64 w))
	13.2b	(-.f64 (+.f64 (.f64 1/2 (.f64 l (pow.f64 w 2))) (+.f64 (.f64 1/6 (.f64 (log.f64 l) (.f64 l (pow.f64 w 3)))) (+.f64 (.f64 1/6 (.f64 (pow.f64 (log.f64 l) 3) (.f64 l (pow.f64 w 3)))) (+.f64 (.f64 (log.f64 l) (.f64 l w)) (+.f64 l (.f64 1/2 (.f64 (pow.f64 (log.f64 l) 2) (.f64 l (pow.f64 w 2))))))))) (+.f64 (.f64 1/6 (.f64 l (pow.f64 w 3))) (+.f64 (.f64 1/2 (.f64 (log.f64 l) (.f64 l (pow.f64 w 2)))) (*.f64 l w))))
	10.0b	(/.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))

Compiler

Compiled 1934 to 718 computations (62.9% saved)

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (exp.f64 w))
✓	0.0b	(/.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (exp.f64 w))
✓	0.2b	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))
✓	0.2b	(pow.f64 l (sqrt.f64 (exp.f64 w)))

series1.7s (5.2%)

Counts

4 → 64

Calls

4 calls:

790.0ms	(/.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (exp.f64 w))
775.0ms	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))
148.0ms	(pow.f64 l (sqrt.f64 (exp.f64 w)))
3.0ms	(sqrt.f64 (exp.f64 w))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`unpow-prod-down_binary64`
38×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
33×	`times-frac_binary64`

Counts

4 → 133

Calls

4 calls:

6.0ms	(/.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (exp.f64 w))
3.0ms	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))
2.0ms	(pow.f64 l (sqrt.f64 (exp.f64 w)))
1.0ms	(sqrt.f64 (exp.f64 w))

simplify146.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

559×	`times-frac_binary64`
320×	`fma-neg_binary64`
176×	`exp-prod_binary64`
165×	`distribute-rgt-out_binary64`
164×	`cancel-sign-sub-inv_binary64`

Counts

197 → 205

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	4070
1	574	3385
2	1992	3340
3	4448	3340
4	4954	3340
5	5013	3340

prune183.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	228	3	231
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	231	4	235

Error

0.0b

Counts

235 → 4

Alt Table

Status	Error	Program
	2.3b	(/.f64 (pow.f64 (expm1.f64 (log1p.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))))) (sqrt.f64 (exp.f64 w))) (exp.f64 w))
	13.2b	(-.f64 (+.f64 (.f64 1/2 (.f64 l (pow.f64 w 2))) (+.f64 (.f64 1/6 (.f64 (log.f64 l) (.f64 l (pow.f64 w 3)))) (+.f64 (.f64 1/6 (.f64 (pow.f64 (log.f64 l) 3) (.f64 l (pow.f64 w 3)))) (+.f64 (.f64 (log.f64 l) (.f64 l w)) (+.f64 l (.f64 1/2 (.f64 (pow.f64 (log.f64 l) 2) (.f64 l (pow.f64 w 2))))))))) (+.f64 (.f64 1/6 (.f64 l (pow.f64 w 3))) (+.f64 (.f64 1/2 (.f64 (log.f64 l) (.f64 l (pow.f64 w 2)))) (*.f64 l w))))
▶	0.7b	(/.f64 (sqrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))) (/.f64 (exp.f64 w) (sqrt.f64 (pow.f64 l (exp.f64 w)))))
	7.9b	(/.f64 (+.f64 (.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l))))) (fma.f64 (log.f64 l) (*.f64 l w) l)) (exp.f64 w))

Compiler

Compiled 5139 to 1422 computations (72.3% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 l (sqrt.f64 (exp.f64 w)))
✓	0.2b	(/.f64 (exp.f64 w) (sqrt.f64 (pow.f64 l (exp.f64 w))))
✓	0.2b	(/.f64 (sqrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))) (/.f64 (exp.f64 w) (sqrt.f64 (pow.f64 l (exp.f64 w)))))
	0.3b	(pow.f64 l (exp.f64 w))

series1.1s (3.4%)

Counts

2 → 48

Calls

2 calls:

942.0ms	(/.f64 (sqrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))) (/.f64 (exp.f64 w) (sqrt.f64 (pow.f64 l (exp.f64 w)))))
183.0ms	(/.f64 (exp.f64 w) (sqrt.f64 (pow.f64 l (exp.f64 w))))

rewrite175.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

956×	`times-frac_binary64`
728×	`sqrt-prod_binary64`
497×	`unpow-prod-down_binary64`
465×	`*-un-lft-identity_binary64`
465×	`add-sqr-sqrt_binary64`

Counts

2 → 598

Calls

2 calls:

19.0ms	(/.f64 (sqrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))) (/.f64 (exp.f64 w) (sqrt.f64 (pow.f64 l (exp.f64 w)))))
5.0ms	(/.f64 (exp.f64 w) (sqrt.f64 (pow.f64 l (exp.f64 w))))

simplify697.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

717×	`associate-/r/_binary64`
483×	`associate-/l/_binary64`
448×	`associate-*l/_binary64`
409×	`associate-/l*_binary64`
222×	`associate-*r/_binary64`

Counts

646 → 736

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	849	38077
1	1648	37598
2	4987	37596
3	5068	37596

prune521.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	795	2	797
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	797	4	801

Error

0.0b

Counts

801 → 4

Alt Table

Status	Error	Program
	2.3b	(/.f64 (pow.f64 (expm1.f64 (log1p.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))))) (sqrt.f64 (exp.f64 w))) (exp.f64 w))
▶	0.7b	(/.f64 (/.f64 (sqrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))) (*.f64 (cbrt.f64 (exp.f64 w)) (cbrt.f64 (exp.f64 w)))) (/.f64 (cbrt.f64 (exp.f64 w)) (sqrt.f64 (pow.f64 l (exp.f64 w)))))
	13.2b	(-.f64 (+.f64 (.f64 (.f64 l (pow.f64 w 3)) (+.f64 (.f64 1/6 (log.f64 l)) (.f64 1/6 (pow.f64 (log.f64 l) 3)))) (fma.f64 1/2 (.f64 l (.f64 w w)) (fma.f64 (log.f64 l) (.f64 l w) (fma.f64 1/2 (.f64 (.f64 l (.f64 w w)) (pow.f64 (log.f64 l) 2)) l)))) (fma.f64 1/6 (.f64 l (pow.f64 w 3)) (fma.f64 l w (.f64 (log.f64 l) (.f64 1/2 (.f64 l (*.f64 w w)))))))
	7.9b	(/.f64 (+.f64 (.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l))))) (fma.f64 (log.f64 l) (*.f64 l w) l)) (exp.f64 w))

Compiler

Compiled 32831 to 5562 computations (83.1% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (cbrt.f64 (exp.f64 w)) (sqrt.f64 (pow.f64 l (exp.f64 w))))
	0.2b	(pow.f64 l (sqrt.f64 (exp.f64 w)))
✓	0.2b	(/.f64 (/.f64 (sqrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))) (*.f64 (cbrt.f64 (exp.f64 w)) (cbrt.f64 (exp.f64 w)))) (/.f64 (cbrt.f64 (exp.f64 w)) (sqrt.f64 (pow.f64 l (exp.f64 w)))))
	0.3b	(pow.f64 l (exp.f64 w))

series1.5s (4.7%)

Counts

2 → 48

Calls

2 calls:

967.0ms

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

580.0ms

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

rewrite562.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

3262×	`times-frac_binary64`
1562×	`sqrt-prod_binary64`
1111×	`*-un-lft-identity_binary64`
1111×	`add-sqr-sqrt_binary64`
1111×	`add-cube-cbrt_binary64`

Counts

2 → 1350

Calls

2 calls:

46.0ms

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

6.0ms

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

simplify1.8s (5.4%)

Algorithm

1×	egg-herbie

Rules

1043×	`associate-/r/_binary64`
907×	`associate-/l/_binary64`
877×	`associate-/l*_binary64`
238×	`times-frac_binary64`
126×	`fma-def_binary64`

Counts

1398 → 1551

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1475	112861
1	3652	111326
2	5401	111326

prune1.2s (3.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	1611	1	1612
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	1612	4	1616

Error

0.0b

Counts

1616 → 4

Alt Table

Status	Error	Program
	2.3b	(/.f64 (pow.f64 (expm1.f64 (log1p.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))))) (sqrt.f64 (exp.f64 w))) (exp.f64 w))
	1.1b	(.f64 (/.f64 (/.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))) (cbrt.f64 (exp.f64 w))) (/.f64 (.f64 (cbrt.f64 (cbrt.f64 (exp.f64 w))) (cbrt.f64 (cbrt.f64 (exp.f64 w)))) (sqrt.f64 (sqrt.f64 (pow.f64 l (exp.f64 w)))))) (/.f64 (/.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))) (cbrt.f64 (exp.f64 w))) (/.f64 (cbrt.f64 (cbrt.f64 (exp.f64 w))) (sqrt.f64 (sqrt.f64 (pow.f64 l (exp.f64 w)))))))
	13.2b	(-.f64 (+.f64 (.f64 (.f64 l (pow.f64 w 3)) (+.f64 (.f64 1/6 (log.f64 l)) (.f64 1/6 (pow.f64 (log.f64 l) 3)))) (fma.f64 1/2 (.f64 l (.f64 w w)) (fma.f64 (log.f64 l) (.f64 l w) (fma.f64 1/2 (.f64 (.f64 l (.f64 w w)) (pow.f64 (log.f64 l) 2)) l)))) (fma.f64 1/6 (.f64 l (pow.f64 w 3)) (fma.f64 l w (.f64 (log.f64 l) (.f64 1/2 (.f64 l (*.f64 w w)))))))
	7.9b	(/.f64 (+.f64 (.f64 (.f64 l (.f64 w w)) (.f64 (log.f64 l) (+.f64 1/2 (log.f64 (sqrt.f64 l))))) (fma.f64 (log.f64 l) (*.f64 l w) l)) (exp.f64 w))

Compiler

Compiled 85689 to 11504 computations (86.6% saved)

regimes739.0ms (2.2%)

Accuracy

Total 0.2b remaining (64.1%)

Threshold costs 0.2b (64.1%)

Counts

253 → 1

Compiler

Compiled 17807 to 9295 computations (47.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`exp-1-e_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	16	23
2	15	23

end97.0ms (0.3%)

Compiler: Compiled 204 to 103 computations (49.5% saved)

Details

analyze2.0s (6.2%)

sample20.0s (60.4%)

simplify90.0ms (0.3%)

prune3.0ms (0%)

localize4.0ms (0%)

series304.0ms (0.9%)

rewrite9.0ms (0%)

simplify81.0ms (0.2%)

prune77.0ms (0.2%)

localize6.0ms (0%)

series1.7s (5.2%)

rewrite20.0ms (0.1%)

simplify146.0ms (0.4%)

prune183.0ms (0.6%)

localize10.0ms (0%)

series1.1s (3.4%)

rewrite175.0ms (0.5%)

simplify697.0ms (2.1%)

prune521.0ms (1.6%)

localize14.0ms (0%)

series1.5s (4.7%)

rewrite562.0ms (1.7%)

simplify1.8s (5.4%)

prune1.2s (3.5%)

regimes739.0ms (2.2%)

simplify2.0ms (0%)

end97.0ms (0.3%)

Profiling