Details

analyze1.1s (4.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
3.1%	96.7%	0.2%	8
4.7%	95.1%	0.2%	9
4.7%	95.1%	0.2%	10
18.7%	81.1%	0.2%	11
24.6%	67.4%	8%	12
28.7%	63.4%	8%	13
28.7%	63.4%	8%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample5.9s (27.1%)

Infinites

0.3% of outputs are infinite.

Results

1.9s	1614×	body	8192	exit
1.2s	1821×	body	1024	valid
901.0ms	3955×	body	128	valid
576.0ms	1442×	body	512	valid
331.0ms	300×	body	2048	valid
275.0ms	1631×	body	128	invalid
190.0ms	738×	body	256	valid
137.0ms	223×	body	1024	invalid
74.0ms	242×	body	512	invalid
38.0ms	188×	body	256	invalid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify249.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

3540×	`fma-neg_binary64`
744×	`div-sub_binary64`
658×	`sub-neg_binary64`
627×	`fma-def_binary64`
613×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	23	18
2	48	17
3	86	17
4	177	14
5	318	14
6	465	14
7	536	14
8	618	14
9	723	14
10	1083	14
11	1710	14
12	1873	14
13	2250	14
14	2803	14
15	3186	14
16	3529	14
17	3735	14
18	3809	14
19	4125	14
20	4337	14
21	3179	14
22	3171	14
23	3183	14
24	3183	14
25	4223	14
26	7145	14

prune3.0ms (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

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 52 to 35 computations (32.7% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	0.0b	(*.f64 y (expm1.f64 z))
✓	3.3b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series1.2s (5.7%)

Counts

3 → 108

Calls

3 calls:

754.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
462.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
6.0ms	(*.f64 y (expm1.f64 z))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-sqr-sqrt_binary64`
57×	`*-un-lft-identity_binary64`
55×	`add-cube-cbrt_binary64`
46×	`times-frac_binary64`
39×	`prod-diff_binary64`

Counts

3 → 120

Calls

3 calls:

6.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
3.0ms	(*.f64 y (expm1.f64 z))
2.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

simplify140.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

368×	`sub-neg_binary64`
214×	`associate-r_binary64`
206×	`times-frac_binary64`
198×	`+-commutative_binary64`
198×	`fma-def_binary64`

Counts

228 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	449	8286
1	1238	5190
2	3933	5134
3	5113	5134

prune190.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	206	7	213
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	206	8	214

Error

0.0b

Counts

214 → 8

Alt Table

Status	Error	Program
	33.5b	(-.f64 x (.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (sqrt.f64 t))))
✓	0.8b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
▶	0.8b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	22.1b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	20.1b	(-.f64 x (*.f64 (/.f64 y t) z))
	22.8b	(-.f64 x (.f64 (sqrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (sqrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	1.1b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	54.7b	(-.f64 (-.f64 x (/.f64 (log.f64 y) t)) (/.f64 (log.f64 (expm1.f64 z)) t))

Compiler

Compiled 7185 to 2350 computations (67.3% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	0.0b	(*.f64 y (expm1.f64 z))
✓	0.6b	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
✓	3.1b	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

series2.2s (10.2%)

Counts

3 → 120

Calls

3 calls:

867.0ms	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
831.0ms	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))
492.0ms	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))

rewrite75.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

354×	`times-frac_binary64`
252×	`add-sqr-sqrt_binary64`
243×	`*-un-lft-identity_binary64`
238×	`add-cube-cbrt_binary64`
132×	`prod-diff_binary64`

Counts

3 → 306

Calls

3 calls:

18.0ms	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
4.0ms	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
2.0ms	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

simplify362.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

346×	`fma-def_binary64`
316×	`associate-/l*_binary64`
295×	`associate-/r*_binary64`
267×	`times-frac_binary64`
204×	`associate-/r/_binary64`

Counts

426 → 468

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	702	23281
1	2004	16368
2	4985	16368
3	4996	16368

prune517.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	497	1	498
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	498	8	506

Error

0.0b

Counts

506 → 8

Alt Table

Status	Error	Program
	33.5b	(-.f64 x (.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (sqrt.f64 t))))
✓	0.8b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	0.8b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	22.1b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	20.1b	(-.f64 x (*.f64 (/.f64 y t) z))
	10.0b	(-.f64 x (/.f64 (expm1.f64 z) (/.f64 t y)))
▶	1.1b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	54.7b	(-.f64 (-.f64 x (/.f64 (log.f64 y) t)) (/.f64 (log.f64 (expm1.f64 z)) t))

Compiler

Compiled 22098 to 8777 computations (60.3% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)))
✓	0.4b	(.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)))
	3.3b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
✓	12.9b	(cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

series4.6s (21.1%)

Counts

3 → 108

Calls

3 calls:

2.2s

(*.f64 (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)))

1.6s

(cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

778.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)))

rewrite42.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`cbrt-prod_binary64`
78×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`

Counts

3 → 160

Calls

3 calls:

13.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)))

10.0ms

(*.f64 (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)))

2.0ms

(cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

simplify267.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

756×	`associate-/l*_binary64`
419×	`*-commutative_binary64`
242×	`+-commutative_binary64`
192×	`fma-def_binary64`
182×	`associate-+r+_binary64`

Counts

268 → 363

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1164	18311
1	3562	16895
2	5831	16895

prune962.0ms (4.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	721	2	723
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	723	8	731

Error

Counts

731 → 8

Alt Table

Status	Error	Program
	33.5b	(-.f64 x (.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (sqrt.f64 t))))
✓	0.8b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	0.8b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	22.1b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
▶	1.1b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 (expm1.f64 z) y))) (cbrt.f64 (log1p.f64 (.f64 (expm1.f64 z) y))))) (cbrt.f64 (/.f64 (cbrt.f64 (log1p.f64 (*.f64 (expm1.f64 z) y))) t)))))
	10.5b	(-.f64 x (*.f64 (/.f64 y t) (expm1.f64 z)))
✓	1.1b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	54.7b	(-.f64 (-.f64 x (/.f64 (log.f64 y) t)) (/.f64 (log.f64 (expm1.f64 z)) t))

Compiler

Compiled 50487 to 20435 computations (59.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.3b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
✓	5.3b	(cbrt.f64 (/.f64 (cbrt.f64 (log1p.f64 (*.f64 (expm1.f64 z) y))) t))
✓	9.7b	(cbrt.f64 (log1p.f64 (*.f64 (expm1.f64 z) y)))
	12.9b	(cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

series2.3s (10.8%)

Counts

2 → 60

Calls

2 calls:

1.7s	(cbrt.f64 (/.f64 (cbrt.f64 (log1p.f64 (*.f64 (expm1.f64 z) y))) t))
662.0ms	(cbrt.f64 (log1p.f64 (*.f64 (expm1.f64 z) y)))

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`cbrt-prod_binary64`
18×	`times-frac_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`

Counts

2 → 46

Calls

2 calls:

2.0ms	(cbrt.f64 (/.f64 (cbrt.f64 (log1p.f64 (*.f64 (expm1.f64 z) y))) t))
1.0ms	(cbrt.f64 (log1p.f64 (*.f64 (expm1.f64 z) y)))

simplify158.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

729×	`fma-def_binary64`
437×	`associate-/l*_binary64`
387×	`times-frac_binary64`
279×	`associate-/r*_binary64`
262×	`*-commutative_binary64`

Counts

106 → 150

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	698	8721
1	2220	8084
2	5222	8084

prune806.0ms (3.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	554	0	554
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	554	8	562

Error

Counts

562 → 8

Alt Table

Status	Error	Program
	33.5b	(-.f64 x (.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (sqrt.f64 t))))
✓	0.8b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	0.8b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	22.1b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
✓	1.1b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 (expm1.f64 z) y))) (cbrt.f64 (log1p.f64 (.f64 (expm1.f64 z) y))))) (cbrt.f64 (/.f64 (cbrt.f64 (log1p.f64 (*.f64 (expm1.f64 z) y))) t)))))
	10.5b	(-.f64 x (*.f64 (/.f64 y t) (expm1.f64 z)))
✓	1.1b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	54.7b	(-.f64 (-.f64 x (/.f64 (log.f64 y) t)) (/.f64 (log.f64 (expm1.f64 z)) t))

Compiler

Compiled 54270 to 20499 computations (62.2% saved)

regimes406.0ms (1.9%)

Accuracy

Total 0.7b remaining (80.5%)

Threshold costs 0.7b (80.5%)

Counts

53 → 1

Compiler

Compiled 11371 to 6587 computations (42.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
2	20	14
3	24	14
4	27	14
5	28	14
6	28	14

end99.0ms (0.5%)

Compiler: Compiled 202 to 113 computations (44.1% saved)

Details

analyze1.1s (4.9%)

sample5.9s (27.1%)

simplify249.0ms (1.2%)

prune3.0ms (0%)

localize7.0ms (0%)

series1.2s (5.7%)

rewrite20.0ms (0.1%)

simplify140.0ms (0.6%)

prune190.0ms (0.9%)

localize8.0ms (0%)

series2.2s (10.2%)

rewrite75.0ms (0.3%)

simplify362.0ms (1.7%)

prune517.0ms (2.4%)

localize10.0ms (0%)

series4.6s (21.1%)

rewrite42.0ms (0.2%)

simplify267.0ms (1.2%)

prune962.0ms (4.5%)

localize19.0ms (0.1%)

series2.3s (10.8%)

rewrite6.0ms (0%)

simplify158.0ms (0.7%)

prune806.0ms (3.7%)

regimes406.0ms (1.9%)

simplify3.0ms (0%)

end99.0ms (0.5%)

Profiling