Details

analyze1.5s (10.1%)

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
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

Compiler

Compiled 32 to 21 computations (34.4% saved)

sample111.0ms (0.8%)

Algorithm

1×

intervals

Results

64.0ms	256×	body	128	valid
8.0ms	37×	body	128	nan

Compiler

Compiled 66 to 44 computations (33.3% saved)

simplify131.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
620×	`associate-/l/_binary64`
557×	`cube-prod_binary64`
533×	`sqr-pow_binary64`
502×	`pow-sqr_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	22
1	28	21
2	34	21
3	45	14
4	62	11
5	65	11
6	176	11
7	479	11
8	769	11
9	839	11
10	1233	11
11	1523	11
12	2341	11
13	3455	11
14	4399	11
15	4874	11
16	4872	11

prune9.0ms (0.1%)

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 (log.f64 (hypot.f64 re im)) (log.f64 base))
	31.8b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))

Status

Error

Program

▶

0.3b

(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

31.8b

(/.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))) (log.f64 base)) (*.f64 (atan2.f64 im re) 0)) (+.f64 (*.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))

Compiler

Compiled 120 to 77 computations (35.8% saved)

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.3b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`times-frac_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
12×	`pow1_binary64`

Counts

2 → 48

Calls

2 calls:

10.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
1.0ms	(hypot.f64 re im)

series1.6s (11%)

Counts

2 → 60

Calls

2 calls:

1.6s	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
27.0ms	(hypot.f64 re im)

simplify175.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

787×	`times-frac_binary64`
599×	`fma-neg_binary64`
441×	`associate-/r*_binary64`
410×	`associate-/l*_binary64`
341×	`fma-def_binary64`

Counts

108 → 206

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	2481
1	484	2312
2	1291	2236
3	4583	2236
4	4984	2236

prune189.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	197	9	206
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	198	10	208

Error

0.0b

Counts

208 → 10

Alt Table

Status	Error	Program
	13.3b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	1.2b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.3b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	1.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 base))))
	33.4b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (log.f64 base))))
	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
▶	0.3b	(*.f64 1 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))
	31.8b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))

Compiler

Compiled 3010 to 1405 computations (53.3% saved)

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
	0.3b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify21.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune208.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	206	10	216

Error

0.0b

Counts

216 → 10

Alt Table

Status	Error	Program
	13.3b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	1.2b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.3b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	1.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 base))))
	33.4b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (log.f64 base))))
▶	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
✓	0.3b	(*.f64 1 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))
	31.8b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))

Compiler

Compiled 3278 to 1676 computations (48.9% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.2b	(/.f64 1 (log.f64 base))
✓	0.3b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
16×	`associate-r_binary64`

Counts

2 → 79

Calls

2 calls:

13.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
10.0ms	(/.f64 1 (log.f64 base))

series2.0s (13.9%)

Counts

2 → 44

Calls

2 calls:

1.6s	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
462.0ms	(/.f64 1 (log.f64 base))

simplify246.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

453×	`div-sub_binary64`
341×	`times-frac_binary64`
295×	`associate-/l*_binary64`
248×	`fma-def_binary64`
229×	`sub-neg_binary64`

Counts

123 → 228

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2246
1	382	1983
2	984	1943
3	3458	1943
4	4757	1943
5	5751	1943

prune267.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	350	2	352
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	352	10	362

Error

0.0b

Counts

362 → 10

Alt Table

Status	Error	Program
	1.2b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.9b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	33.4b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	1.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 base))))
	33.4b	(.f64 (.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (/.f64 1 (log.f64 base)))) (sqrt.f64 (/.f64 1 (log.f64 base))))
	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (log.f64 base))))
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
▶	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
✓	0.3b	(*.f64 1 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))
	31.8b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))

Compiler

Compiled 3810 to 1943 computations (49% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im)))
✓	0.5b	(*.f64 (log.f64 base) (log.f64 base))
✓	0.5b	(*.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im)))
✓	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))

rewrite54.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`pow1_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`log-prod_binary64`

Counts

4 → 130

Calls

4 calls:

15.0ms	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
10.0ms	(.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im)))
8.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im)))
7.0ms	(*.f64 (log.f64 base) (log.f64 base))

series2.3s (15.8%)

Counts

4 → 96

Calls

4 calls:

1.7s	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
429.0ms	(*.f64 (log.f64 base) (log.f64 base))
128.0ms	(.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im)))
99.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im)))

simplify294.0ms (2%)

Algorithm

1×	egg-herbie

Rules

325×	`fma-neg_binary64`
300×	`fma-def_binary64`
269×	`associate-r_binary64`
227×	`+-commutative_binary64`
209×	`times-frac_binary64`

Counts

226 → 420

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	466	6108
1	1297	5533
2	4584	5369
3	4972	5369

prune458.0ms (3.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	417	3	420
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	419	11	430

Error

Counts

430 → 11

Alt Table

Status	Error	Program
	1.2b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	34.6b	(pow.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))) 1/3)
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	0.7b	(*.f64 (log.f64 (hypot.f64 im re)) (cbrt.f64 (/.f64 1 (pow.f64 (log.f64 base) 3))))
	0.9b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	33.4b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	1.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 base))))
✓	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
✓	0.3b	(*.f64 1 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))
	31.8b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
	0.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im)))) (cbrt.f64 (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))

Compiler

Compiled 10934 to 4424 computations (59.5% saved)

regimes1.6s (10.9%)

Accuracy

Total 0.3b remaining (89.5%)

Threshold costs 0.3b (89.5%)

Compiler

Compiled 15816 to 9916 computations (37.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	8	11

end16.0ms (0.1%)

Remove: (sort re im)
Compiler: Compiled 30 to 21 computations (30% saved)

sample3.4s (22.7%)

Algorithm

1×

intervals

Results

2.3s	8000×	body	128	valid
247.0ms	1081×	body	128	nan

Compiler

Compiled 269 to 159 computations (40.9% saved)

Details

analyze1.5s (10.1%)

sample111.0ms (0.8%)

simplify131.0ms (0.9%)

prune9.0ms (0.1%)

localize15.0ms (0.1%)

rewrite16.0ms (0.1%)

series1.6s (11%)

simplify175.0ms (1.2%)

prune189.0ms (1.3%)

localize16.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify21.0ms (0.1%)

prune208.0ms (1.4%)

localize16.0ms (0.1%)

rewrite31.0ms (0.2%)

series2.0s (13.9%)

simplify246.0ms (1.7%)

prune267.0ms (1.8%)

localize27.0ms (0.2%)

rewrite54.0ms (0.4%)

series2.3s (15.8%)

simplify294.0ms (2%)

prune458.0ms (3.1%)

regimes1.6s (10.9%)

simplify5.0ms (0%)

end16.0ms (0.1%)

sample3.4s (22.7%)

Profiling