Details

analyze745.0ms (7.7%)

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)

sample57.0ms (0.6%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
4.0ms	36×	body	128	nan

Compiler

Compiled 66 to 44 computations (33.3% 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%)

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))
	30.9b	(/.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))

30.9b

(/.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)

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))

series695.0ms (7.2%)

Counts

1 → 36

Calls

1 calls:

695.0ms

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

rewrite5.0ms (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))

simplify93.0ms (1%)

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

prune65.0ms (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
	32.7b	(/.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))))
	14.2b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (hypot.f64 im re)) (log.f64 base)) 3))
	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	14.9b	(.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))))
	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))))
	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))))
▶	0.3b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))
	1.2b	(/.f64 (*.f64 (cbrt.f64 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 base) (cbrt.f64 (log.f64 (hypot.f64 re im)))))
	0.4b	(*.f64 (log.f64 (hypot.f64 re im)) (/.f64 1 (log.f64 base)))

Compiler

Compiled 2262 to 984 computations (56.5% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series802.0ms (8.3%)

Counts

1 → 36

Calls

1 calls:

802.0ms

(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

124×	`times-frac_binary64`
58×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
58×	`add-cube-cbrt_binary64`
33×	`pow1_binary64`

Counts

1 → 102

Calls

1 calls:

6.0ms

(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))

simplify161.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

725×	`times-frac_binary64`
405×	`associate-/l*_binary64`
328×	`associate-/r*_binary64`
289×	`distribute-rgt-neg-in_binary64`
253×	`fma-def_binary64`

Counts

138 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	3407
1	381	3130
2	1067	3090
3	3870	3089
4	4852	3089
5	4986	3089
6	4928	3089

prune108.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	152	9	161

Error

0.0b

Counts

161 → 9

Alt Table

Status	Error	Program
	0.6b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
▶	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	14.9b	(.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))))
	1.3b	(/.f64 (/.f64 (/.f64 (log.f64 (hypot.f64 re im)) 1) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.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))))
	0.7b	(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))))
✓	0.3b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))
	14.2b	(/.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 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 base) (cbrt.f64 (log.f64 (hypot.f64 re im)))))

Compiler

Compiled 3494 to 1534 computations (56.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	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)))

series1.5s (15.7%)

Counts

2 → 72

Calls

2 calls:

805.0ms	(/.f64 (log.f64 base) (log.f64 (hypot.f64 re im)))
716.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))

rewrite26.0ms (0.3%)

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)))

simplify148.0ms (1.5%)

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

prune205.0ms (2.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	238	2	240
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	238	11	249

Error

Counts

249 → 11

Alt Table

Status	Error	Program
▶	0.6b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
✓	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	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 1 (/.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (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))))
	14.9b	(.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))))
	1.3b	(/.f64 (/.f64 (/.f64 (log.f64 (hypot.f64 re im)) 1) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	0.7b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) 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))))
✓	0.3b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))
	14.2b	(/.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 (log.f64 (hypot.f64 re im))) (cbrt.f64 (log.f64 (hypot.f64 re im)))) (/.f64 (log.f64 base) (cbrt.f64 (log.f64 (hypot.f64 re im)))))

Compiler

Compiled 7050 to 3406 computations (51.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series2.4s (24.3%)

Counts

3 → 80

Calls

3 calls:

1.6s	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
733.0ms	(pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base)))
44.0ms	(/.f64 1 (log.f64 base))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64`
23×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
16×	`pow-unpow_binary64`

Counts

3 → 90

Calls

3 calls:

3.0ms	(pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base)))
2.0ms	(/.f64 1 (log.f64 base))
2.0ms	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))

simplify178.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

341×	`fma-neg_binary64`
331×	`times-frac_binary64`
291×	`associate-/r*_binary64`
238×	`associate-/l*_binary64`
217×	`sub-neg_binary64`

Counts

170 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	340	5176
1	1069	4758
2	4256	4586
3	4405	4570
4	4932	4570
5	4819	4570

prune181.0ms (1.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	207	11	218

Error

Counts

218 → 11

Alt Table

Status	Error	Program
✓	0.6b	(log.f64 (pow.f64 (hypot.f64 im re) (/.f64 1 (log.f64 base))))
✓	0.4b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))))
	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 1 (/.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (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))))
	14.9b	(.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 (/.f64 (log.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im)))) (log.f64 base)) (/.f64 (log.f64 (cbrt.f64 (hypot.f64 re im))) (log.f64 base)))
	1.3b	(/.f64 (/.f64 (/.f64 (log.f64 (hypot.f64 re im)) 1) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	0.7b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (log.f64 (hypot.f64 re im))) 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))))
✓	0.3b	(/.f64 (/.f64 (log.f64 (hypot.f64 re im)) 1) (log.f64 base))
	14.2b	(/.f64 (sqrt.f64 (log.f64 (hypot.f64 re im))) (/.f64 (log.f64 base) (sqrt.f64 (log.f64 (hypot.f64 re im)))))

Compiler

Compiled 5884 to 3282 computations (44.2% saved)

regimes553.0ms (5.7%)

Accuracy

Total 0.3b remaining (91.6%)

Threshold costs 0.3b (91.6%)

Counts

115 → 1

Compiler

Compiled 10396 to 6711 computations (35.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	8	11

end8.0ms (0.1%)

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

sample1.6s (16.5%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
119.0ms	1027×	body	128	nan

Compiler

Compiled 267 to 154 computations (42.3% saved)

Details

analyze745.0ms (7.7%)

sample57.0ms (0.6%)

simplify96.0ms (1%)

prune5.0ms (0%)

localize8.0ms (0.1%)

series695.0ms (7.2%)

rewrite5.0ms (0.1%)

simplify93.0ms (1%)

prune65.0ms (0.7%)

localize8.0ms (0.1%)

series802.0ms (8.3%)

rewrite18.0ms (0.2%)

simplify161.0ms (1.7%)

prune108.0ms (1.1%)

localize8.0ms (0.1%)

series1.5s (15.7%)

rewrite26.0ms (0.3%)

simplify148.0ms (1.5%)

prune205.0ms (2.1%)

localize10.0ms (0.1%)

series2.4s (24.3%)

rewrite11.0ms (0.1%)

simplify178.0ms (1.8%)

prune181.0ms (1.9%)

regimes553.0ms (5.7%)

simplify2.0ms (0%)

end8.0ms (0.1%)

sample1.6s (16.5%)

Profiling