Details

analyze600.0ms (10.8%)

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)

sample133.0ms (2.4%)

Algorithm

1×

intervals

Results

35.0ms	256×	body	128	valid
4.0ms	32×	body	128	nan

Compiler

Compiled 66 to 44 computations (33.3% saved)

simplify124.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1042×	`fma-def_binary64`
693×	`fma-neg_binary64`
662×	`cube-prod_binary64`
522×	`pow-sqr_binary64`
453×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	20
1	35	19
2	57	12
3	80	9
4	89	9
5	216	9
6	486	9
7	978	9
8	1296	9
9	1996	9
10	2287	9
11	3311	9
12	4367	9
13	4644	9
14	4721	9
15	4986	9
16	4826	9

prune4.0ms (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 (atan2.f64 im re) (log.f64 base))
	30.4b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))

Status

Error

Program

▶

0.3b

(/.f64 (atan2.f64 im re) (log.f64 base))

30.4b

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

Compiler

Compiled 117 to 73 computations (37.6% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

series405.0ms (7.3%)

Counts

1 → 8

Calls

1 calls:

405.0ms

(/.f64 (atan2.f64 im re) (log.f64 base))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 33

Calls

1 calls:

2.0ms

(/.f64 (atan2.f64 im re) (log.f64 base))

simplify87.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

763×	`fma-neg_binary64`
574×	`neg-mul-1_binary64`
543×	`neg-sub0_binary64`
429×	`sub-neg_binary64`
336×	`div-sub_binary64`

Counts

41 → 35

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	663
1	108	615
2	213	585
3	384	585
4	1312	585
5	2948	585
6	3524	585
7	4593	585
8	4969	585

prune37.0ms (0.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	22	13	35
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	23	14	37

Error

0.0b

Counts

37 → 14

Alt Table

Status	Error	Program
	8.0b	(cbrt.f64 (/.f64 (.f64 (.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
	30.4b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	0.8b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	8.0b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
	33.7b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	1.2b	(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	31.7b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
▶	0.3b	(*.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))
	33.7b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))
	32.2b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	29.6b	(.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
	1.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))

Compiler

Compiled 973 to 392 computations (59.7% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

prune33.0ms (0.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	35	14	49

Error

0.0b

Counts

49 → 14

Alt Table

Status	Error	Program
	8.0b	(cbrt.f64 (/.f64 (.f64 (.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
	30.4b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
▶	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	0.8b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	8.0b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
	33.7b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	1.2b	(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	31.7b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
✓	0.3b	(*.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))
	33.7b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))
	32.2b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	29.6b	(.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
	1.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))

Compiler

Compiled 1032 to 454 computations (56% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (log.f64 base))
✓	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))

series427.0ms (7.7%)

Counts

2 → 44

Calls

2 calls:

393.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
33.0ms	(/.f64 1 (log.f64 base))

rewrite12.0ms (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 → 78

Calls

2 calls:

6.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
3.0ms	(/.f64 1 (log.f64 base))

simplify91.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

460×	`unsub-neg_binary64`
434×	`div-sub_binary64`
409×	`sub-neg_binary64`
351×	`associate-*r/_binary64`
251×	`times-frac_binary64`

Counts

122 → 97

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	1290
1	145	1159
2	320	1159
3	749	1159
4	1828	1159
5	3850	1159
6	4946	1159

prune82.0ms (1.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	3	9	12
Picked	0	1	1
Done	0	1	1
Total	96	15	111

Error

0.0b

Counts

111 → 15

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
▶	0.8b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	8.0b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
	8.0b	(cbrt.f64 (.f64 (.f64 (.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)) (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
	1.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
	1.2b	(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	31.7b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	30.4b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
✓	0.3b	(*.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))
	32.2b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	29.6b	(.f64 (/.f64 (sqrt.f64 (atan2.f64 im re)) (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (sqrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
	33.7b	(.f64 (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 base)))) (sqrt.f64 (/.f64 1 (log.f64 base))))
	1.5b	(.f64 (.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base))))) (cbrt.f64 (/.f64 1 (log.f64 base))))
	33.7b	(*.f64 (atan2.f64 im re) (/.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base))))

Compiler

Compiled 1911 to 899 computations (53% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (log.f64 base) (atan2.f64 im re))
✓	0.7b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))

series807.0ms (14.5%)

Counts

2 → 44

Calls

2 calls:

404.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))
403.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
60×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64`

Counts

2 → 123

Calls

2 calls:

5.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
2.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

simplify139.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

991×	`div-sub_binary64`
742×	`fma-neg_binary64`
273×	`times-frac_binary64`
234×	`neg-mul-1_binary64`
167×	`*-commutative_binary64`

Counts

167 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	2859
1	193	2535
2	462	2498
3	1252	2498
4	2721	2498
5	4977	2498
6	5528	2498

prune102.0ms (1.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	140	5	145
Fresh	5	7	12
Picked	1	0	1
Done	0	2	2
Total	146	14	160

Error

0.0b

Counts

160 → 14

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (cbrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	33.9b	(/.f64 (/.f64 1 (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
	33.7b	(.f64 (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 base)))) (sqrt.f64 (/.f64 1 (log.f64 base))))
	1.6b	(/.f64 1 (/.f64 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base)))))
	8.0b	(cbrt.f64 (.f64 (.f64 (.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)) (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
	1.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (log.f64 base))))
	1.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))) (/.f64 1 (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))))
	30.4b	(/.f64 (-.f64 (.f64 (atan2.f64 im re) (log.f64 base)) (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
✓	0.3b	(*.f64 1 (/.f64 (atan2.f64 im re) (log.f64 base)))
	7.9b	(/.f64 1 (cbrt.f64 (.f64 (.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) (/.f64 (log.f64 base) (atan2.f64 im re))) (/.f64 (log.f64 base) (atan2.f64 im re)))))
	13.9b	(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (atan2.f64 im re)))))
	1.5b	(.f64 (.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base))))) (cbrt.f64 (/.f64 1 (log.f64 base))))
	33.7b	(*.f64 (atan2.f64 im re) (/.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base))))

Compiler

Compiled 2768 to 942 computations (66% saved)

regimes535.0ms (9.6%)

Accuracy

Total 0.3b remaining (88.4%)

Threshold costs 0.3b (88.4%)

Counts

98 → 1

Compiler

Compiled 9316 to 5601 computations (39.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end1.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample1.9s (34.1%)

Algorithm

1×

intervals

Results

1.3s	8000×	body	128	valid
114.0ms	966×	body	128	nan

Compiler

Compiled 349 to 199 computations (43% saved)

Details

analyze600.0ms (10.8%)

sample133.0ms (2.4%)

simplify124.0ms (2.2%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series405.0ms (7.3%)

rewrite4.0ms (0.1%)

simplify87.0ms (1.6%)

prune37.0ms (0.7%)

localize8.0ms (0.1%)

prune33.0ms (0.6%)

localize8.0ms (0.1%)

series427.0ms (7.7%)

rewrite12.0ms (0.2%)

simplify91.0ms (1.6%)

prune82.0ms (1.5%)

localize6.0ms (0.1%)

series807.0ms (14.5%)

rewrite20.0ms (0.4%)

simplify139.0ms (2.5%)

prune102.0ms (1.8%)

regimes535.0ms (9.6%)

simplify2.0ms (0%)

end1.0ms (0%)

sample1.9s (34.1%)

Profiling