Details

analyze1.2s (16.2%)

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)

sample2.0s (26.6%)

Results

1.7s	8256×	body	128	valid
226.0ms	1001×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify126.0ms (1.7%)

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

Status

Error

Program

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)))

▶

0.3b

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

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))

series439.0ms (5.9%)

Counts

1 → 8

Calls

1 calls:

439.0ms

(/.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))

simplify85.0ms (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

prune39.0ms (0.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	23	12	35
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	23	14	37

Error

0.0b

Counts

37 → 14

Alt Table

Status	Error	Program
	1.2b	(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	1.4b	(.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))))
	1.7b	(/.f64 (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (log.f64 base) (cbrt.f64 (atan2.f64 im re))))
	6.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 (atan2.f64 im re) (log.f64 base))) (/.f64 (atan2.f64 im re) (log.f64 base))))
▶	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	32.4b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	31.8b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (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)))
	33.5b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))))
	1.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	32.8b	(.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))))
	32.7b	(/.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)))
	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 988 to 384 computations (61.1% saved)

localize7.0ms (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))

series442.0ms (5.9%)

Counts

2 → 44

Calls

2 calls:

407.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
35.0ms	(/.f64 1 (log.f64 base))

rewrite14.0ms (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))

simplify83.0ms (1.1%)

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

prune80.0ms (1.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	5	7	12
Picked	0	1	1
Done	0	1	1
Total	99	13	112

Error

0.0b

Counts

112 → 13

Alt Table

Status	Error	Program
	33.6b	(.f64 (atan2.f64 im re) (.f64 (sqrt.f64 (/.f64 1 (log.f64 base))) (sqrt.f64 (/.f64 1 (log.f64 base)))))
▶	0.5b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	33.6b	(.f64 (.f64 (atan2.f64 im re) (/.f64 1 (sqrt.f64 (log.f64 base)))) (/.f64 1 (sqrt.f64 (log.f64 base))))
	0.7b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	1.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	31.8b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
✓	0.3b	(/.f64 (atan2.f64 im re) (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)))
	6.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 (atan2.f64 im re) (log.f64 base))) (/.f64 (atan2.f64 im re) (log.f64 base))))
✓	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	1.5b	(.f64 (atan2.f64 im re) (.f64 (*.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base)))) (cbrt.f64 (/.f64 1 (log.f64 base)))))
	32.8b	(.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))))
	32.7b	(/.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 1834 to 862 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))
✓	0.4b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))

series787.0ms (10.6%)

Counts

2 → 44

Calls

2 calls:

394.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))
392.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))

rewrite25.0ms (0.3%)

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))

simplify125.0ms (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

prune117.0ms (1.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	140	5	145
Fresh	3	7	10
Picked	0	1	1
Done	1	1	2
Total	144	14	158

Error

0.0b

Counts

158 → 14

Alt Table

Status	Error	Program
	12.1b	(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (atan2.f64 im re)))))
	1.2b	(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	33.6b	(.f64 (atan2.f64 im re) (.f64 (sqrt.f64 (/.f64 1 (log.f64 base))) (sqrt.f64 (/.f64 1 (log.f64 base)))))
▶	0.6b	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (atan2.f64 im re)))
✓	0.5b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	33.6b	(.f64 (.f64 (atan2.f64 im re) (/.f64 1 (sqrt.f64 (log.f64 base)))) (/.f64 1 (sqrt.f64 (log.f64 base))))
	0.7b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	32.6b	(/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (atan2.f64 im re)))) (/.f64 (log.f64 base) (sqrt.f64 (atan2.f64 im re))))
	31.8b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	6.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) (/.f64 (atan2.f64 im re) (log.f64 base))) (/.f64 (atan2.f64 im re) (log.f64 base))))
	32.8b	(.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))))
	1.4b	(.f64 (/.f64 1 (/.f64 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))) 1)) (/.f64 1 (/.f64 (cbrt.f64 (log.f64 base)) (atan2.f64 im re))))
	33.6b	(/.f64 1 (/.f64 (sqrt.f64 (log.f64 base)) (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base)))))

Compiler

Compiled 2921 to 1047 computations (64.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (atan2.f64 im re))
	0.3b	(/.f64 1 (log.f64 base))
✓	0.5b	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (atan2.f64 im re)))

series406.0ms (5.5%)

Counts

2 → 36

Calls

2 calls:

393.0ms	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (atan2.f64 im re)))
13.0ms	(/.f64 1 (atan2.f64 im re))

rewrite60.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

538×	`times-frac_binary64`
241×	`*-un-lft-identity_binary64`
241×	`add-sqr-sqrt_binary64`
241×	`add-cube-cbrt_binary64`
46×	`add-exp-log_binary64`

Counts

2 → 304

Calls

2 calls:

10.0ms	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (atan2.f64 im re)))
2.0ms	(/.f64 1 (atan2.f64 im re))

simplify378.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

486×	`fma-neg_binary64`
409×	`neg-mul-1_binary64`
378×	`neg-sub0_binary64`
351×	`unsub-neg_binary64`
311×	`times-frac_binary64`

Counts

340 → 289

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	7681
1	324	6875
2	759	6740
3	1429	6740
4	1668	6740
5	3348	6740
6	4148	6740
7	4413	6740
8	4994	6740
9	4847	6740

prune243.0ms (3.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	324	4	328
Fresh	8	3	11
Picked	0	1	1
Done	0	2	2
Total	332	10	342

Error

Counts

342 → 10

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (atan2.f64 im re)))
	1.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base)))) 1) (/.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (/.f64 1 (atan2.f64 im re))))
✓	0.5b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	0.7b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	1.4b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (/.f64 1 (atan2.f64 im re)) (/.f64 1 (cbrt.f64 (log.f64 base)))))
	34.7b	(/.f64 (/.f64 1 (log.f64 base)) (*.f64 (sqrt.f64 (/.f64 1 (atan2.f64 im re))) (sqrt.f64 (/.f64 1 (atan2.f64 im re)))))
	32.8b	(.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))))
	31.8b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	6.4b	(/.f64 (/.f64 1 (log.f64 base)) (cbrt.f64 (pow.f64 (/.f64 1 (atan2.f64 im re)) 3)))

Compiler

Compiled 7412 to 3921 computations (47.1% saved)

regimes635.0ms (8.5%)

Accuracy

Total 0.3b remaining (90.2%)

Threshold costs 0.3b (90.2%)

Counts

119 → 1

Compiler

Compiled 11261 to 7501 computations (33.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end138.0ms (1.9%)

Compiler: Compiled 196 to 130 computations (33.7% saved)

Details

analyze1.2s (16.2%)

sample2.0s (26.6%)

simplify126.0ms (1.7%)

prune5.0ms (0.1%)

localize5.0ms (0.1%)

series439.0ms (5.9%)

rewrite4.0ms (0.1%)

simplify85.0ms (1.1%)

prune39.0ms (0.5%)

localize7.0ms (0.1%)

series442.0ms (5.9%)

rewrite14.0ms (0.2%)

simplify83.0ms (1.1%)

prune80.0ms (1.1%)

localize6.0ms (0.1%)

series787.0ms (10.6%)

rewrite25.0ms (0.3%)

simplify125.0ms (1.7%)

prune117.0ms (1.6%)

localize8.0ms (0.1%)

series406.0ms (5.5%)

rewrite60.0ms (0.8%)

simplify378.0ms (5.1%)

prune243.0ms (3.3%)

regimes635.0ms (8.5%)

simplify2.0ms (0%)

end138.0ms (1.9%)

Profiling