Details

analyze1.8s (22.2%)

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
0%	74.9%	25.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
0%	62.4%	37.6%	10
0.6%	61.8%	37.6%	11
0.9%	61.5%	37.6%	12
1%	55.1%	43.8%	13
1.5%	54.6%	43.8%	14

Compiler

Compiled 32 to 21 computations (34.4% saved)

sample2.0s (24%)

Results

1.7s	8256×	body	128	valid
195.0ms	1003×	body	128	invalid

Compiler

Compiled 63 to 41 computations (34.9% saved)

simplify134.0ms (1.6%)

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

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
▶	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	32.7b	(/.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))

32.7b

(/.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)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series441.0ms (5.4%)

Counts

1 → 8

Calls

1 calls:

440.0ms

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

rewrite4.0ms (0%)

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))

simplify90.0ms (1.1%)

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

prune34.0ms (0.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	24	11	35
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	25	12	37

Error

0.1b

Counts

37 → 12

Alt Table

Status	Error	Program
	32.3b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	9.2b	(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))))
▶	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	0.5b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	30.7b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	1.6b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	30.0b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	32.3b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))
	1.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	30.9b	(.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))))
	32.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (sqrt.f64 (log.f64 base))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (sqrt.f64 (log.f64 base))))

Compiler

Compiled 858 to 326 computations (62% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series467.0ms (5.7%)

Counts

2 → 44

Calls

2 calls:

433.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
34.0ms	(/.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 → 78

Calls

2 calls:

6.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
2.0ms	(/.f64 1 (log.f64 base))

simplify96.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

460×	`unsub-neg_binary64`
434×	`div-sub_binary64`
409×	`sub-neg_binary64`
377×	`associate-*r/_binary64`
274×	`associate-/l*_binary64`

Counts

122 → 98

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	1290
1	145	1159
2	320	1159
3	749	1159
4	1826	1159
5	3850	1159
6	4946	1159

prune84.0ms (1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	7	3	10
Picked	0	1	1
Done	0	1	1
Total	98	12	110

Error

0.0b

Counts

110 → 12

Alt Table

Status	Error	Program
	32.4b	(.f64 (.f64 (atan2.f64 im re) (/.f64 1 (sqrt.f64 (log.f64 base)))) (/.f64 1 (sqrt.f64 (log.f64 base))))
	1.1b	(.f64 (atan2.f64 im re) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base))))
✓	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
▶	0.5b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	32.3b	(.f64 (atan2.f64 im re) (.f64 (sqrt.f64 (/.f64 1 (log.f64 base))) (sqrt.f64 (/.f64 1 (log.f64 base)))))
	1.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (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))))
	32.3b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	0.7b	(.f64 (atan2.f64 im re) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
	1.6b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (*.f64 (cbrt.f64 (atan2.f64 im re)) (/.f64 1 (log.f64 base))))
	0.7b	(.f64 (atan2.f64 im re) (cbrt.f64 (.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))))

Compiler

Compiled 1776 to 846 computations (52.4% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (log.f64 base) (atan2.f64 im re))
✓	0.4b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))

series825.0ms (10%)

Counts

2 → 44

Calls

2 calls:

413.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
411.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

rewrite17.0ms (0.2%)

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

simplify140.0ms (1.7%)

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

prune115.0ms (1.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	138	7	145
Fresh	4	5	9
Picked	1	0	1
Done	0	2	2
Total	143	14	157

Error

0.0b

Counts

157 → 14

Alt Table

Status	Error	Program
	1.3b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))) (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
	1.1b	(.f64 (atan2.f64 im re) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base))))
	12.7b	(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (atan2.f64 im re)))))
✓	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	33.8b	(/.f64 1 (expm1.f64 (log1p.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))))
	1.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	32.4b	(/.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (sqrt.f64 (log.f64 base)) (atan2.f64 im re)))
▶	0.7b	(.f64 (atan2.f64 im re) (cbrt.f64 (.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))))
	30.6b	(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (atan2.f64 im re)))) (/.f64 1 (/.f64 (log.f64 base) (sqrt.f64 (atan2.f64 im re)))))
	9.1b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 3)))
	32.3b	(.f64 (atan2.f64 im re) (.f64 (sqrt.f64 (/.f64 1 (log.f64 base))) (sqrt.f64 (/.f64 1 (log.f64 base)))))
	0.7b	(.f64 (atan2.f64 im re) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
	32.4b	(/.f64 1 (*.f64 (sqrt.f64 (log.f64 base)) (/.f64 (sqrt.f64 (log.f64 base)) (atan2.f64 im re))))

Compiler

Compiled 2929 to 1069 computations (63.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 1 (log.f64 base))
✓	0.4b	(.f64 (.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))
✓	0.5b	(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base)))
✓	0.6b	(cbrt.f64 (.f64 (.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base))))

series144.0ms (1.8%)

Counts

3 → 36

Calls

3 calls:

60.0ms

(*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))

51.0ms

(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base)))

33.0ms

(cbrt.f64 (*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base))))

rewrite70.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

292×	`add-exp-log_binary64`
148×	`prod-exp_binary64`
114×	`div-exp_binary64`
86×	`times-frac_binary64`
79×	`pow1_binary64`

Counts

3 → 279

Calls

3 calls:

14.0ms

(*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))

12.0ms

(*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base)))

10.0ms

(cbrt.f64 (*.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base))))

simplify185.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

637×	`unswap-sqr_binary64`
617×	`fma-def_binary64`
462×	`times-frac_binary64`
440×	`log-prod_binary64`
326×	`associate-l_binary64`

Counts

315 → 314

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	4566
1	266	3148
2	615	2838
3	2185	2707
4	3828	2707
5	4984	2707
6	4952	2707

prune386.0ms (4.7%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	429	2	431
Fresh	1	10	11
Picked	0	1	1
Done	0	2	2
Total	430	15	445

Error

0.0b

Counts

445 → 15

Alt Table

Status	Error	Program
	1.3b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))) (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))) (cbrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
	1.1b	(.f64 (atan2.f64 im re) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base))))
	30.6b	(*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (atan2.f64 im re)))) (/.f64 1 (/.f64 (log.f64 base) (sqrt.f64 (atan2.f64 im re)))))
	1.0b	(.f64 (atan2.f64 im re) (.f64 (cbrt.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base)))) (cbrt.f64 (/.f64 1 (log.f64 base)))))
	12.7b	(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (atan2.f64 im re)))))
✓	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	33.8b	(/.f64 1 (expm1.f64 (log1p.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))))
	1.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	32.4b	(/.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (sqrt.f64 (log.f64 base)) (atan2.f64 im re)))
✓	0.7b	(.f64 (atan2.f64 im re) (cbrt.f64 (.f64 (*.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (log.f64 base))) (/.f64 1 (log.f64 base)))))
	32.4b	(/.f64 1 (*.f64 (sqrt.f64 (log.f64 base)) (/.f64 (sqrt.f64 (log.f64 base)) (atan2.f64 im re))))
	0.7b	(*.f64 (atan2.f64 im re) (cbrt.f64 (/.f64 1 (pow.f64 (log.f64 base) 3))))
	9.1b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 3)))
	32.3b	(.f64 (atan2.f64 im re) (.f64 (sqrt.f64 (/.f64 1 (log.f64 base))) (sqrt.f64 (/.f64 1 (log.f64 base)))))

Compiler

Compiled 10490 to 5702 computations (45.6% saved)

regimes958.0ms (11.7%)

Accuracy

Total 0.3b remaining (85.7%)

Threshold costs 0.3b (85.7%)

Counts

175 → 1

Compiler

Compiled 16816 to 11371 computations (32.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end181.0ms (2.2%)

Compiler: Compiled 276 to 179 computations (35.1% saved)

Details

analyze1.8s (22.2%)

sample2.0s (24%)

simplify134.0ms (1.6%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series441.0ms (5.4%)

rewrite4.0ms (0%)

simplify90.0ms (1.1%)

prune34.0ms (0.4%)

localize6.0ms (0.1%)

series467.0ms (5.7%)

rewrite12.0ms (0.1%)

simplify96.0ms (1.2%)

prune84.0ms (1%)

localize9.0ms (0.1%)

series825.0ms (10%)

rewrite17.0ms (0.2%)

simplify140.0ms (1.7%)

prune115.0ms (1.4%)

localize10.0ms (0.1%)

series144.0ms (1.8%)

rewrite70.0ms (0.8%)

simplify185.0ms (2.3%)

prune386.0ms (4.7%)

regimes958.0ms (11.7%)

simplify2.0ms (0%)

end181.0ms (2.2%)

Profiling