Details

analyze503.0ms (8.2%)

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)

sample1.7s (27.5%)

Infinites

0% of outputs are infinite.

Results

1.4s	8256×	body	128	valid
170.0ms	1081×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify125.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	30.0b	(/.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))

30.0b

(/.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))

series431.0ms (7%)

Counts

1 → 8

Calls

1 calls:

431.0ms

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

rewrite5.0ms (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:

3.0ms

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

simplify87.0ms (1.4%)

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 (0.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	27	8	35
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	27	10	37

Error

0.0b

Counts

37 → 10

Alt Table

Status	Error	Program
	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))))
	30.0b	(/.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)))
	30.3b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	8.3b	(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))))
	36.0b	(/.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)))
▶	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	0.6b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	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))))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

Compiler

Compiled 822 to 310 computations (62.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series437.0ms (7.1%)

Counts

2 → 44

Calls

2 calls:

404.0ms	(*.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)))
2.0ms	(/.f64 1 (log.f64 base))

simplify86.0ms (1.4%)

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

prune74.0ms (1.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	96	11	107

Error

Counts

107 → 11

Alt Table

Status	Error	Program
	36.0b	(*.f64 (atan2.f64 im re) (/.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base))))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	0.7b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	36.0b	(.f64 (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 base)))) (sqrt.f64 (/.f64 1 (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))))
	30.0b	(/.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)))
	30.3b	(*.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) (/.f64 1 (log.f64 base)))
▶	0.6b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	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))))
	8.3b	(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)))))

Compiler

Compiled 1747 to 815 computations (53.3% 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))
✓	0.5b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))

series773.0ms (12.6%)

Counts

2 → 44

Calls

2 calls:

392.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
380.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

rewrite20.0ms (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)))
2.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

simplify133.0ms (2.2%)

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

prune95.0ms (1.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	145	11	156

Error

Counts

156 → 11

Alt Table

Status	Error	Program
	36.0b	(*.f64 (atan2.f64 im re) (/.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base))))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
▶	0.7b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	36.0b	(.f64 (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 base)))) (sqrt.f64 (/.f64 1 (log.f64 base))))
	30.3b	(*.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) (/.f64 1 (log.f64 base)))
✓	0.6b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	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))))
	33.0b	(/.f64 1 (expm1.f64 (log1p.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))))
	8.3b	(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)))))
	8.2b	(/.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)))))

Compiler

Compiled 2804 to 977 computations (65.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 1 (log.f64 base))
✓	0.3b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
✓	0.7b	(cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3))
✓	0.7b	(pow.f64 (/.f64 1 (log.f64 base)) 3)

series465.0ms (7.6%)

Counts

3 → 60

Calls

3 calls:

392.0ms	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
40.0ms	(pow.f64 (/.f64 1 (log.f64 base)) 3)
33.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`cbrt-prod_binary64`
76×	`times-frac_binary64`
75×	`add-sqr-sqrt_binary64`
58×	`*-un-lft-identity_binary64`
56×	`add-cube-cbrt_binary64`

Counts

3 → 175

Calls

3 calls:

13.0ms	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
6.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3))
4.0ms	(pow.f64 (/.f64 1 (log.f64 base)) 3)

simplify133.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

823×	`fma-def_binary64`
457×	`associate-/r/_binary64`
319×	`times-frac_binary64`
250×	`log-prod_binary64`
210×	`unswap-sqr_binary64`

Counts

235 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	2917
1	244	2623
2	739	2574
3	2121	2574
4	4620	2574
5	5343	2574

prune148.0ms (2.4%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	2	5	7
Picked	0	1	1
Done	0	3	3
Total	208	10	218

Error

Counts

218 → 10

Alt Table

Status	Error	Program
✓	0.7b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	36.0b	(.f64 (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 base)))) (sqrt.f64 (/.f64 1 (log.f64 base))))
	30.3b	(*.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) (/.f64 1 (log.f64 base)))
✓	0.6b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	0.8b	(.f64 (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))) (cbrt.f64 (.f64 (/.f64 1 (log.f64 base)) (/.f64 1 (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))))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	8.3b	(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)))))
	8.2b	(/.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)))))

Compiler

Compiled 3781 to 2205 computations (41.7% saved)

regimes715.0ms (11.6%)

Accuracy

Total 0.2b remaining (80.5%)

Threshold costs 0.2b (80.5%)

Counts

131 → 1

Compiler

Compiled 12641 to 8176 computations (35.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end118.0ms (1.9%)

Compiler: Compiled 196 to 119 computations (39.3% saved)

Details

analyze503.0ms (8.2%)

sample1.7s (27.5%)

simplify125.0ms (2%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series431.0ms (7%)

rewrite5.0ms (0.1%)

simplify87.0ms (1.4%)

prune34.0ms (0.5%)

localize6.0ms (0.1%)

series437.0ms (7.1%)

rewrite12.0ms (0.2%)

simplify86.0ms (1.4%)

prune74.0ms (1.2%)

localize6.0ms (0.1%)

series773.0ms (12.6%)

rewrite20.0ms (0.3%)

simplify133.0ms (2.2%)

prune95.0ms (1.5%)

localize9.0ms (0.1%)

series465.0ms (7.6%)

rewrite37.0ms (0.6%)

simplify133.0ms (2.2%)

prune148.0ms (2.4%)

regimes715.0ms (11.6%)

simplify2.0ms (0%)

end118.0ms (1.9%)

Profiling