Details

analyze1.6s (21.2%)

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)

sample2.1s (27.1%)

Results

1.7s	8256×	body	128	valid
236.0ms	1068×	body	128	invalid

Compiler

Compiled 63 to 41 computations (34.9% saved)

simplify124.0ms (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

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
	34.5b	(/.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

34.5b

(/.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))

series424.0ms (5.5%)

Counts

1 → 8

Calls

1 calls:

424.0ms

(/.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))

simplify89.0ms (1.2%)

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

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	25	10	35
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	25	12	37

Error

0.0b

Counts

37 → 12

Alt Table

Status	Error	Program
	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	34.5b	(/.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)))
	1.6b	(.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))))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	8.8b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
	29.8b	(/.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)))
▶	0.4b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	31.5b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))
	32.7b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	8.8b	(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))))

Compiler

Compiled 870 to 338 computations (61.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
✓	0.3b	(/.f64 (log.f64 base) (atan2.f64 im re))

series867.0ms (11.3%)

Counts

2 → 44

Calls

2 calls:

454.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
413.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

rewrite30.0ms (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:

12.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))
5.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))

simplify134.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

167 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	2835
1	193	2535
2	462	2498
3	1252	2498
4	2721	2498
5	4977	2498
6	5528	2498

prune124.0ms (1.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	138	5	143
Fresh	4	6	10
Picked	0	1	1
Done	0	1	1
Total	142	13	155

Error

Counts

155 → 13

Alt Table

Status	Error	Program
▶	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	34.5b	(/.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 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	29.8b	(/.f64 1 (*.f64 (sqrt.f64 (log.f64 base)) (/.f64 (sqrt.f64 (log.f64 base)) (atan2.f64 im re))))
	8.8b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.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)))))
	13.3b	(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (atan2.f64 im re)))))
	1.2b	(.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))))
	1.2b	(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	31.5b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))
	8.8b	(/.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)))))
	32.7b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

Compiler

Compiled 2893 to 1026 computations (64.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series461.0ms (6%)

Counts

2 → 44

Calls

2 calls:

422.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
38.0ms	(/.f64 1 (log.f64 base))

rewrite13.0ms (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)))
2.0ms	(/.f64 1 (log.f64 base))

simplify82.0ms (1.1%)

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

prune73.0ms (0.9%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	9	10
Picked	0	1	1
Done	0	2	2
Total	97	13	110

Error

Counts

110 → 13

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	34.5b	(/.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 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	29.8b	(/.f64 1 (*.f64 (sqrt.f64 (log.f64 base)) (/.f64 (sqrt.f64 (log.f64 base)) (atan2.f64 im re))))
	8.8b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.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)))))
	13.3b	(/.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)))
	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
▶	0.8b	(.f64 (atan2.f64 im re) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
	31.5b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))
	8.8b	(/.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)))))
	32.7b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

Compiler

Compiled 1802 to 837 computations (53.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))
✓	0.4b	(.f64 (atan2.f64 im re) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
✓	0.6b	(*.f64 (log.f64 base) (log.f64 base))
✓	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))

series509.0ms (6.6%)

Counts

4 → 72

Calls

4 calls:

420.0ms	(.f64 (atan2.f64 im re) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
35.0ms	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
29.0ms	(.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))
25.0ms	(*.f64 (log.f64 base) (log.f64 base))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
16×	`associate-r_binary64`

Counts

4 → 119

Calls

4 calls:

9.0ms	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
5.0ms	(.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))
5.0ms	(.f64 (atan2.f64 im re) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
4.0ms	(*.f64 (log.f64 base) (log.f64 base))

simplify103.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

349×	`associate-/l/_binary64`
328×	`distribute-rgt-in_binary64`
302×	`distribute-lft-in_binary64`
281×	`log-prod_binary64`
258×	`associate-/r/_binary64`

Counts

191 → 169

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	142	2157
1	248	1930
2	698	1912
3	1677	1867
4	3818	1863
5	4907	1863

prune137.0ms (1.8%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	1	8	9
Picked	0	1	1
Done	0	3	3
Total	169	13	182

Error

Counts

182 → 13

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	34.5b	(/.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 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	29.8b	(/.f64 1 (*.f64 (sqrt.f64 (log.f64 base)) (/.f64 (sqrt.f64 (log.f64 base)) (atan2.f64 im re))))
	8.8b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.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)))))
	13.3b	(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (atan2.f64 im re)))))
	0.7b	(/.f64 (atan2.f64 im re) (cbrt.f64 (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base))))
	32.7b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.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)))
	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
✓	0.8b	(.f64 (atan2.f64 im re) (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (*.f64 (log.f64 base) (log.f64 base)) (log.f64 base)))))
	31.5b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

Compiler

Compiled 4296 to 2185 computations (49.1% saved)

regimes559.0ms (7.2%)

Accuracy

Total 0.3b remaining (84.7%)

Threshold costs 0.3b (84.7%)

Counts

105 → 1

Compiler

Compiled 9896 to 6506 computations (34.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end148.0ms (1.9%)

Compiler: Compiled 248 to 149 computations (39.9% saved)

Details

analyze1.6s (21.2%)

sample2.1s (27.1%)

simplify124.0ms (1.6%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series424.0ms (5.5%)

rewrite4.0ms (0.1%)

simplify89.0ms (1.2%)

prune39.0ms (0.5%)

localize6.0ms (0.1%)

series867.0ms (11.3%)

rewrite30.0ms (0.4%)

simplify134.0ms (1.7%)

prune124.0ms (1.6%)

localize7.0ms (0.1%)

series461.0ms (6%)

rewrite13.0ms (0.2%)

simplify82.0ms (1.1%)

prune73.0ms (0.9%)

localize11.0ms (0.1%)

series509.0ms (6.6%)

rewrite30.0ms (0.4%)

simplify103.0ms (1.3%)

prune137.0ms (1.8%)

regimes559.0ms (7.2%)

simplify2.0ms (0%)

end148.0ms (1.9%)

Profiling