Details

analyze599.0ms (5.3%)

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)

sample2.5s (21.8%)

Symmetry

(sort re im)

Results

2.1s	8256×	body	128	valid
276.0ms	1047×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify95.0ms (0.8%)

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%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	28.8b	(/.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)))
▶	0.3b	(/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))

Status

Error

Program

28.8b

(/.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)))

▶

0.3b

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

Compiler

Compiled 120 to 77 computations (35.8% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series710.0ms (6.3%)

Counts

1 → 36

Calls

1 calls:

709.0ms

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 38

Calls

1 calls:

3.0ms

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

simplify89.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-neg_binary64`
369×	`div-sub_binary64`
319×	`times-frac_binary64`
242×	`associate-/l*_binary64`
231×	`associate-/r*_binary64`

Counts

74 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	1913
1	345	1739
2	855	1699
3	2882	1699
4	4710	1699
5	5508	1699

prune74.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	82	11	93
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Error

0.0b

Counts

95 → 11

Alt Table

Status	Error	Program
	17.2b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.9b	(log1p.f64 (expm1.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)))
	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	(cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	35.7b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))
	1.5b	(.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))))
	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)))
	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))))
	35.8b	(*.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))))
	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

Compiler

Compiled 2272 to 978 computations (57% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series742.0ms (6.6%)

Counts

2 → 44

Calls

2 calls:

708.0ms	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))
34.0ms	(/.f64 1 (log.f64 base))

rewrite16.0ms (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))

simplify99.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

453×	`div-sub_binary64`
341×	`times-frac_binary64`
294×	`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	4563	1943
5	5555	1943

prune118.0ms (1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	139	13	152

Error

0.0b

Counts

152 → 13

Alt Table

Status	Error	Program
	17.2b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.9b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.5b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	1.6b	(.f64 (log.f64 (hypot.f64 re im)) (.f64 (*.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base)))) (cbrt.f64 (/.f64 1 (log.f64 base)))))
✓	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (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	(cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	35.7b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))
	0.7b	(.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)))))
	0.7b	(*.f64 (log.f64 (hypot.f64 re im)) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	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))))
	35.8b	(*.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))))
▶	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

Compiler

Compiled 3037 to 1486 computations (51.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series1.4s (12.5%)

Counts

2 → 72

Calls

2 calls:

758.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
655.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

rewrite22.0ms (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)))

simplify146.0ms (1.3%)

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

prune214.0ms (1.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	237	3	240
Fresh	3	8	11
Picked	1	0	1
Done	1	0	1
Total	242	11	253

Error

Counts

253 → 11

Alt Table

Status	Error	Program
▶	0.4b	(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (/.f64 1 (log.f64 (hypot.f64 re im)))))
	0.6b	(cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	1.3b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))) (/.f64 (cbrt.f64 (log.f64 base)) (log.f64 (hypot.f64 re im)))))
	35.7b	(exp.f64 (log.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base))))
	17.2b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.9b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.5b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	1.6b	(.f64 (log.f64 (hypot.f64 re im)) (.f64 (*.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base)))) (cbrt.f64 (/.f64 1 (log.f64 base)))))
	0.6b	(/.f64 1 (cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	35.8b	(*.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))))
	0.7b	(.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 7062 to 3434 computations (51.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series825.0ms (7.3%)

Counts

3 → 84

Calls

3 calls:

729.0ms	(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (/.f64 1 (log.f64 (hypot.f64 re im)))))
68.0ms	(/.f64 1 (log.f64 (hypot.f64 re im)))
28.0ms	(/.f64 1 (/.f64 1 (log.f64 (hypot.f64 re im))))

rewrite150.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

248×	`times-frac_binary64`
174×	`add-sqr-sqrt_binary64`
171×	`add-exp-log_binary64`
132×	`*-un-lft-identity_binary64`
110×	`add-cube-cbrt_binary64`

Counts

3 → 301

Calls

3 calls:

21.0ms	(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (/.f64 1 (log.f64 (hypot.f64 re im)))))
5.0ms	(/.f64 1 (/.f64 1 (log.f64 (hypot.f64 re im))))
2.0ms	(/.f64 1 (log.f64 (hypot.f64 re im)))

simplify247.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

533×	`fma-neg_binary64`
350×	`sub-neg_binary64`
269×	`associate-/r*_binary64`
244×	`times-frac_binary64`
213×	`fma-def_binary64`

Counts

385 → 493

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	466	7920
1	1264	7356
2	4129	7320
3	4925	7288
4	4987	7288

prune508.0ms (4.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	531	1	532
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	532	11	543

Error

Counts

543 → 11

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (/.f64 1 (log.f64 (hypot.f64 re im)))))
	0.6b	(cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base)) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))) (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	17.2b	(*.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (/.f64 (sqrt.f64 (log.f64 (hypot.f64 im re))) (log.f64 base)))
	0.9b	(log1p.f64 (expm1.f64 (/.f64 (log.f64 (hypot.f64 re im)) (log.f64 base))))
	0.5b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
	1.6b	(.f64 (log.f64 (hypot.f64 re im)) (.f64 (*.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base)))) (cbrt.f64 (/.f64 1 (log.f64 base)))))
	0.6b	(/.f64 1 (cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))))
	35.8b	(*.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))))
	1.3b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))) (/.f64 (cbrt.f64 (log.f64 base)) (log.f64 (hypot.f64 re im)))))
	0.8b	(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 (hypot.f64 im re))) 3))))
	0.7b	(.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 13191 to 7627 computations (42.2% saved)

regimes2.6s (22.6%)

Accuracy

Total 0.3b remaining (90.9%)

Threshold costs 0.3b (90.9%)

Counts

318 → 1

Compiler

Compiled 29871 to 21541 computations (27.9% 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	11	11
1	14	11
2	12	11

end158.0ms (1.4%)

Remove: (sort re im)
Compiler: Compiled 261 to 161 computations (38.3% saved)

Details

analyze599.0ms (5.3%)

sample2.5s (21.8%)

simplify95.0ms (0.8%)

prune5.0ms (0%)

localize8.0ms (0.1%)

series710.0ms (6.3%)

rewrite8.0ms (0.1%)

simplify89.0ms (0.8%)

prune74.0ms (0.7%)

localize8.0ms (0.1%)

series742.0ms (6.6%)

rewrite16.0ms (0.1%)

simplify99.0ms (0.9%)

prune118.0ms (1%)

localize8.0ms (0.1%)

series1.4s (12.5%)

rewrite22.0ms (0.2%)

simplify146.0ms (1.3%)

prune214.0ms (1.9%)

localize12.0ms (0.1%)

series825.0ms (7.3%)

rewrite150.0ms (1.3%)

simplify247.0ms (2.2%)

prune508.0ms (4.5%)

regimes2.6s (22.6%)

simplify2.0ms (0%)

end158.0ms (1.4%)

Profiling