Details

analyze532.0ms (6.5%)

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)

sample158.0ms (1.9%)

Algorithm

1×

intervals

Symmetry

(sort re im)

Results

56.0ms	256×	body	128	valid
3.0ms	32×	body	128	nan

Compiler

Compiled 66 to 44 computations (33.3% saved)

simplify90.0ms (1.1%)

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

prune5.0ms (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
	30.6b	(/.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)))
▶	0.3b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Status

Error

Program

30.6b

(/.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)))

▶

0.3b

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

Compiler

Compiled 120 to 77 computations (35.8% saved)

localize7.0ms (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))

series693.0ms (8.5%)

Counts

2 → 60

Calls

2 calls:

680.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
12.0ms	(hypot.f64 re im)

rewrite5.0ms (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:

3.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
0.0ms	(hypot.f64 re im)

simplify85.0ms (1%)

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 → 142

Iterations

Useful iterations: 2 (0.0ms)

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

prune99.0ms (1.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	129	13	142
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	131	13	144

Error

0.0b

Counts

144 → 13

Alt Table

Status	Error	Program
	18.5b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	1.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.2b	(.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (cbrt.f64 (log.f64 (hypot.f64 im re)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	32.7b	(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	18.5b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.7b	(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))))
	0.6b	(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	19.0b	(.f64 (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 base))))
▶	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	33.7b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))))
	15.9b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (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))))

Compiler

Compiled 3114 to 1441 computations (53.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.2b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
✓	0.4b	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

series1.3s (16.4%)

Counts

2 → 72

Calls

2 calls:

691.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
647.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64`
69×	`*-un-lft-identity_binary64`
69×	`add-sqr-sqrt_binary64`
69×	`add-cube-cbrt_binary64`
45×	`pow1_binary64`

Counts

2 → 144

Calls

2 calls:

5.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
3.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

simplify149.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

432×	`fma-neg_binary64`
429×	`times-frac_binary64`
347×	`associate-/r*_binary64`
294×	`associate-/l*_binary64`
190×	`fma-def_binary64`

Counts

216 → 240

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	394	6731
1	1231	5978
2	4749	5978
3	5095	5978

prune258.0ms (3.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	284	4	288
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	287	14	301

Error

0.0b

Counts

301 → 14

Alt Table

Status	Error	Program
	18.5b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	1.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)))) (cbrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.7b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) 3)))
	15.9b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.2b	(.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (cbrt.f64 (log.f64 (hypot.f64 im re)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	32.7b	(*.f64 (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (sqrt.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))))) (/.f64 1 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	18.5b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.7b	(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))))
	0.6b	(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
▶	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	30.6b	(/.f64 1 (*.f64 -1 (/.f64 (log.f64 (/.f64 1 base)) (log.f64 (sqrt.f64 (+.f64 (pow.f64 re 2) (pow.f64 im 2)))))))
	0.5b	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))
	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))))

Compiler

Compiled 8049 to 4004 computations (50.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series687.0ms (8.4%)

Counts

2 → 44

Calls

2 calls:

656.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
31.0ms	(/.f64 1 (log.f64 base))

rewrite12.0ms (0.1%)

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:

6.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
2.0ms	(/.f64 1 (log.f64 base))

simplify113.0ms (1.4%)

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 → 141

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

prune157.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	184	5	189
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	193	10	203

Error

Counts

203 → 10

Alt Table

Status	Error	Program
	0.7b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) 3)))
	15.9b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.2b	(.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (cbrt.f64 (log.f64 (hypot.f64 im re)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.8b	(.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))))
▶	0.3b	(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
	1.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))))) (/.f64 1 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	18.5b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.6b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	1.3b	(.f64 (log.f64 (hypot.f64 re im)) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base))))
	0.8b	(.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))

Compiler

Compiled 3826 to 1957 computations (48.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series644.0ms (7.9%)

Counts

2 → 60

Calls

2 calls:

631.0ms	(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
13.0ms	(hypot.f64 im re)

rewrite5.0ms (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:

3.0ms	(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
0.0ms	(hypot.f64 im re)

simplify97.0ms (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 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	2493
1	484	2316
2	1291	2236
3	4583	2236
4	4984	2236

prune93.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	142	10	152

Error

Counts

152 → 10

Alt Table

Status	Error	Program
	0.7b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) 3)))
	15.9b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.2b	(.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (cbrt.f64 (log.f64 (hypot.f64 im re)))) (/.f64 (cbrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.8b	(.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))))
✓	0.3b	(/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))
	1.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))))) (/.f64 1 (cbrt.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	18.5b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.6b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	1.3b	(.f64 (log.f64 (hypot.f64 re im)) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base))))
	0.8b	(.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))

Compiler

Compiled 2813 to 1295 computations (54% saved)

regimes1.3s (16%)

Accuracy

Total 0.3b remaining (89.1%)

Threshold costs 0.3b (89.1%)

Counts

200 → 1

Compiler

Compiled 16751 to 11586 computations (30.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	13	11
2	12	11

end8.0ms (0.1%)

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

sample1.6s (19.5%)

Algorithm

1×

intervals

Results

993.0ms	8000×	body	128	valid
130.0ms	966×	body	128	nan

Compiler

Compiled 234 to 145 computations (38% saved)

Details

analyze532.0ms (6.5%)

sample158.0ms (1.9%)

simplify90.0ms (1.1%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

series693.0ms (8.5%)

rewrite5.0ms (0.1%)

simplify85.0ms (1%)

prune99.0ms (1.2%)

localize9.0ms (0.1%)

series1.3s (16.4%)

rewrite19.0ms (0.2%)

simplify149.0ms (1.8%)

prune258.0ms (3.1%)

localize9.0ms (0.1%)

series687.0ms (8.4%)

rewrite12.0ms (0.1%)

simplify113.0ms (1.4%)

prune157.0ms (1.9%)

localize7.0ms (0.1%)

series644.0ms (7.9%)

rewrite5.0ms (0.1%)

simplify97.0ms (1.2%)

prune93.0ms (1.1%)

regimes1.3s (16%)

simplify2.0ms (0%)

end8.0ms (0.1%)

sample1.6s (19.5%)

Profiling