Details

analyze592.0ms (5.8%)

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)

sample1.9s (18.9%)

Results

1.6s	8256×	body	128	valid
199.0ms	1047×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify125.0ms (1.2%)

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

prune5.0ms (0%)

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))
	28.5b	(/.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)))

Status

Error

Program

▶

0.3b

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

28.5b

(/.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)))

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))

series462.0ms (4.5%)

Counts

1 → 8

Calls

1 calls:

462.0ms

(/.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 (0.9%)

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

prune33.0ms (0.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	26	9	35
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	26	11	37

Error

0.1b

Counts

37 → 11

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	6.7b	(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))))
	1.2b	(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
	6.7b	(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))))
	13.2b	(log.f64 (exp.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	0.6b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	1.8b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	28.5b	(/.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)))
	33.0b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (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))))

Compiler

Compiled 850 to 318 computations (62.6% 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)))

series472.0ms (4.6%)

Counts

2 → 44

Calls

2 calls:

437.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
35.0ms	(/.f64 1 (log.f64 base))

rewrite13.0ms (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))

simplify93.0ms (0.9%)

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

prune79.0ms (0.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	94	14	108

Error

0.0b

Counts

108 → 14

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	6.7b	(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))))
	33.1b	(.f64 (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 base)))) (sqrt.f64 (/.f64 1 (log.f64 base))))
	28.5b	(/.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)))
	1.5b	(.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))))
	33.0b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	30.9b	(.f64 (sqrt.f64 (atan2.f64 im re)) (.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 1 (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)))
	6.7b	(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)))))
	13.2b	(log.f64 (exp.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
▶	0.6b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	33.3b	(*.f64 (atan2.f64 im re) (exp.f64 (neg.f64 (log.f64 (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))))

Compiler

Compiled 1845 to 869 computations (52.9% saved)

localize8.0ms (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)))

series1.5s (14.1%)

Counts

2 → 44

Calls

2 calls:

1.0s	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
420.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

rewrite23.0ms (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:

6.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))
5.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))

simplify136.0ms (1.3%)

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

prune114.0ms (1.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	3	8	11
Picked	0	1	1
Done	0	2	2
Total	146	13	159

Error

0.0b

Counts

159 → 13

Alt Table

Status	Error	Program
	33.1b	(.f64 (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 base)))) (sqrt.f64 (/.f64 1 (log.f64 base))))
	28.5b	(/.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)))
▶	1.5b	(.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))))
	33.0b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	6.9b	(/.f64 1 (cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base)) (.f64 (.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)))))
	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))))
	6.7b	(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)))))
✓	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	6.8b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 3)))
✓	0.6b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	33.3b	(*.f64 (atan2.f64 im re) (exp.f64 (neg.f64 (log.f64 (log.f64 base)))))
	30.9b	(.f64 (sqrt.f64 (atan2.f64 im re)) (.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 1 (log.f64 base))))

Compiler

Compiled 2918 to 1049 computations (64.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (atan2.f64 im re) (.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base)))))
✓	0.4b	(.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))))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base))))
✓	0.7b	(cbrt.f64 (/.f64 1 (log.f64 base)))

series3.2s (31.3%)

Counts

4 → 96

Calls

4 calls:

2.0s	(.f64 (atan2.f64 im re) (.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base)))))
498.0ms	(*.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base))))
423.0ms	(.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))))
325.0ms	(cbrt.f64 (/.f64 1 (log.f64 base)))

rewrite64.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`cbrt-prod_binary64`
103×	`add-sqr-sqrt_binary64`
100×	`times-frac_binary64`
78×	`*-un-lft-identity_binary64`
62×	`add-cube-cbrt_binary64`

Counts

4 → 201

Calls

4 calls:

16.0ms	(.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))))
13.0ms	(*.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base))))
8.0ms	(.f64 (atan2.f64 im re) (.f64 (cbrt.f64 (/.f64 1 (log.f64 base))) (cbrt.f64 (/.f64 1 (log.f64 base)))))
2.0ms	(cbrt.f64 (/.f64 1 (log.f64 base)))

simplify217.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

577×	`fma-def_binary64`
499×	`unswap-sqr_binary64`
426×	`times-frac_binary64`
418×	`*-commutative_binary64`
250×	`associate-l_binary64`

Counts

297 → 253

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	5485
1	297	4824
2	1034	4586
3	2675	4540
4	4730	4540
5	5076	4540

prune269.0ms (2.6%)

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	310	1	311
Fresh	0	9	9
Picked	0	1	1
Done	0	3	3
Total	310	14	324

Error

Counts

324 → 14

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	1.1b	(.f64 (.f64 (atan2.f64 im re) (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))))) (cbrt.f64 (/.f64 1 (log.f64 base))))
	33.1b	(.f64 (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 base)))) (sqrt.f64 (/.f64 1 (log.f64 base))))
	28.5b	(/.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)))
✓	1.5b	(.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))))
	33.0b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	6.9b	(/.f64 1 (cbrt.f64 (/.f64 (.f64 (.f64 (log.f64 base) (log.f64 base)) (log.f64 base)) (.f64 (.f64 (atan2.f64 im re) (atan2.f64 im re)) (atan2.f64 im re)))))
	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))))
	6.7b	(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)))))
✓	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	6.8b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 3)))
✓	0.6b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	33.3b	(*.f64 (atan2.f64 im re) (exp.f64 (neg.f64 (log.f64 (log.f64 base)))))
	30.9b	(.f64 (sqrt.f64 (atan2.f64 im re)) (.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 1 (log.f64 base))))

Compiler

Compiled 8876 to 5242 computations (40.9% saved)

regimes664.0ms (6.5%)

Accuracy

Total 0.3b remaining (83.1%)

Threshold costs 0.3b (83.1%)

Counts

120 → 1

Compiler

Compiled 12711 to 8296 computations (34.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end177.0ms (1.7%)

Compiler: Compiled 283 to 175 computations (38.2% saved)

Details

analyze592.0ms (5.8%)

sample1.9s (18.9%)

simplify125.0ms (1.2%)

prune5.0ms (0%)

localize6.0ms (0.1%)

series462.0ms (4.5%)

rewrite4.0ms (0%)

simplify90.0ms (0.9%)

prune33.0ms (0.3%)

localize6.0ms (0.1%)

series472.0ms (4.6%)

rewrite13.0ms (0.1%)

simplify93.0ms (0.9%)

prune79.0ms (0.8%)

localize8.0ms (0.1%)

series1.5s (14.1%)

rewrite23.0ms (0.2%)

simplify136.0ms (1.3%)

prune114.0ms (1.1%)

localize11.0ms (0.1%)

series3.2s (31.3%)

rewrite64.0ms (0.6%)

simplify217.0ms (2.1%)

prune269.0ms (2.6%)

regimes664.0ms (6.5%)

simplify2.0ms (0%)

end177.0ms (1.7%)

Profiling