Details

analyze512.0ms (5.2%)

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
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)

sample1.8s (18.3%)

Symmetry

(sort re im)

Results

1.5s	8256×	body	128	valid
166.0ms	991×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify96.0ms (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
▶	0.4b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
	34.0b	(/.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

▶

0.4b

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

34.0b

(/.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)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series699.0ms (7.2%)

Counts

2 → 60

Calls

2 calls:

686.0ms	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))
12.0ms	(hypot.f64 re im)

rewrite6.0ms (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)

simplify91.0ms (0.9%)

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

prune102.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	131	11	142
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	132	12	144

Error

0.0b

Counts

144 → 12

Alt Table

Status	Error	Program
	1.6b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
▶	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	13.0b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (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))))
	33.3b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	13.0b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	1.0b	(log.f64 (exp.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	13.5b	(.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))))
	17.6b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	34.0b	(/.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)))
	0.7b	(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))))

Compiler

Compiled 3052 to 1437 computations (52.9% saved)

localize10.0ms (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))))
✓	0.3b	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))

series1.7s (17.6%)

Counts

2 → 72

Calls

2 calls:

955.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
759.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

rewrite24.0ms (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)))

simplify141.0ms (1.4%)

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

prune241.0ms (2.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	284	4	288
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	288	12	300

Error

0.0b

Counts

300 → 12

Alt Table

Status	Error	Program
	1.6b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
✓	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	0.7b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (/.f64 (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base)) (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))))))
	0.7b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) 3)))
	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	1.3b	(.f64 (/.f64 1 (/.f64 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))) 1)) (/.f64 1 (/.f64 (cbrt.f64 (log.f64 base)) (log.f64 (hypot.f64 re im)))))
▶	0.4b	(/.f64 1 (*.f64 (log.f64 base) (/.f64 1 (log.f64 (hypot.f64 re im)))))
	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))))
	13.5b	(.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))))
	17.6b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	13.0b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	13.0b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))

Compiler

Compiled 7935 to 3959 computations (50.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series1.5s (15.4%)

Counts

3 → 96

Calls

3 calls:

763.0ms	(*.f64 (log.f64 base) (/.f64 1 (log.f64 (hypot.f64 re im))))
680.0ms	(/.f64 1 (*.f64 (log.f64 base) (/.f64 1 (log.f64 (hypot.f64 re im)))))
64.0ms	(/.f64 1 (log.f64 (hypot.f64 re im)))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-exp-log_binary64`
30×	`add-sqr-sqrt_binary64`
29×	`times-frac_binary64`
24×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`

Counts

3 → 121

Calls

3 calls:

12.0ms	(/.f64 1 (*.f64 (log.f64 base) (/.f64 1 (log.f64 (hypot.f64 re im)))))
7.0ms	(*.f64 (log.f64 base) (/.f64 1 (log.f64 (hypot.f64 re im))))
3.0ms	(/.f64 1 (log.f64 (hypot.f64 re im)))

simplify154.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

695×	`times-frac_binary64`
597×	`associate-/r*_binary64`
488×	`associate-/l*_binary64`
322×	`fma-def_binary64`
202×	`fma-neg_binary64`

Counts

217 → 290

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	529	6930
1	1729	6232
2	4787	6230
3	4976	6230

prune327.0ms (3.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	335	3	338
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	338	12	350

Error

Counts

350 → 12

Alt Table

Status	Error	Program
	1.6b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
✓	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
▶	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	1.3b	(.f64 (/.f64 1 (/.f64 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))) 1)) (/.f64 1 (/.f64 (cbrt.f64 (log.f64 base)) (log.f64 (hypot.f64 re im)))))
	0.7b	(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (log.f64 (hypot.f64 re im))))))
	13.5b	(.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))))
	0.7b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (/.f64 (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base)) (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))))))
	17.6b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	13.0b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.7b	(/.f64 1 (*.f64 (log.f64 base) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 (hypot.f64 re im))) 3))))
	1.3b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))) (*.f64 (cbrt.f64 (log.f64 base)) (/.f64 1 (log.f64 (hypot.f64 re im))))))
	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))))

Compiler

Compiled 10213 to 6091 computations (40.4% 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))
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))

series755.0ms (7.7%)

Counts

2 → 44

Calls

2 calls:

718.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
36.0ms	(/.f64 1 (log.f64 base))

rewrite15.0ms (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:

7.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
3.0ms	(/.f64 1 (log.f64 base))

simplify99.0ms (1%)

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

prune152.0ms (1.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	190	11	201

Error

Counts

201 → 11

Alt Table

Status	Error	Program
	1.6b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
✓	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
	1.3b	(.f64 (/.f64 1 (/.f64 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))) 1)) (/.f64 1 (/.f64 (cbrt.f64 (log.f64 base)) (log.f64 (hypot.f64 re im)))))
	1.0b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	13.5b	(.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))))
	0.7b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (/.f64 (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base)) (.f64 (.f64 (log.f64 (hypot.f64 re im)) (log.f64 (hypot.f64 re im))) (log.f64 (hypot.f64 re im))))))
	13.0b	(.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 1 (log.f64 base))))
	17.6b	(expm1.f64 (log1p.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.7b	(/.f64 1 (*.f64 (log.f64 base) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 (hypot.f64 re im))) 3))))
	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))))

Compiler

Compiled 3655 to 1857 computations (49.2% saved)

regimes1.1s (11.2%)

Accuracy

Total 0.3b remaining (88.8%)

Threshold costs 0.3b (88.8%)

Counts

193 → 1

Compiler

Compiled 16861 to 11816 computations (29.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	10	15

end167.0ms (1.7%)

Remove: (sort re im)
Compiler: Compiled 255 to 164 computations (35.7% saved)

Details

analyze512.0ms (5.2%)

sample1.8s (18.3%)

simplify96.0ms (1%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

series699.0ms (7.2%)

rewrite6.0ms (0.1%)

simplify91.0ms (0.9%)

prune102.0ms (1%)

localize10.0ms (0.1%)

series1.7s (17.6%)

rewrite24.0ms (0.2%)

simplify141.0ms (1.4%)

prune241.0ms (2.5%)

localize9.0ms (0.1%)

series1.5s (15.4%)

rewrite30.0ms (0.3%)

simplify154.0ms (1.6%)

prune327.0ms (3.3%)

localize9.0ms (0.1%)

series755.0ms (7.7%)

rewrite15.0ms (0.2%)

simplify99.0ms (1%)

prune152.0ms (1.6%)

regimes1.1s (11.2%)

simplify2.0ms (0%)

end167.0ms (1.7%)

Profiling