Details

analyze665.0ms (10.8%)

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)

sample147.0ms (2.4%)

Algorithm

1×

intervals

Results

35.0ms	256×	body	128	valid
5.0ms	41×	body	128	nan

Compiler

Compiled 66 to 44 computations (33.3% saved)

simplify150.0ms (2.4%)

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))
	31.6b	(/.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))

31.6b

(/.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))

series495.0ms (8%)

Counts

1 → 8

Calls

1 calls:

495.0ms

(/.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:

3.0ms

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

simplify107.0ms (1.7%)

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

prune42.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	23	12	35
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	24	13	37

Error

0.1b

Counts

37 → 13

Alt Table

Status	Error	Program
	31.2b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.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))))
▶	0.3b	(/.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))
	27.6b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	7.6b	(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))))
	7.6b	(cbrt.f64 (pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 3))
	29.1b	(/.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (log.f64 base) (sqrt.f64 (atan2.f64 im re))))
	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	0.8b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	31.6b	(/.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)))
	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	29.3b	(.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))))
	1.8b	(.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 953 to 376 computations (60.5% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series465.0ms (7.5%)

Counts

1 → 36

Calls

1 calls:

465.0ms

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

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`times-frac_binary64`
83×	`distribute-lft-neg-in_binary64`
83×	`distribute-rgt-neg-in_binary64`
73×	`*-un-lft-identity_binary64`
73×	`add-sqr-sqrt_binary64`

Counts

1 → 158

Calls

1 calls:

6.0ms

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

simplify252.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

737×	`div-sub_binary64`
596×	`neg-mul-1_binary64`
552×	`sub-neg_binary64`
504×	`associate-/l*_binary64`
478×	`associate-/r*_binary64`

Counts

194 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	4170
1	377	4053
2	1272	3906
3	3045	3906
4	4062	3906
5	4157	3906
6	4781	3906
7	4805	3906

prune124.0ms (2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	177	14	191

Error

0.0b

Counts

191 → 14

Alt Table

Status	Error	Program
	32.3b	(*.f64 (sqrt.f64 (neg.f64 (atan2.f64 im re))) (/.f64 (sqrt.f64 (neg.f64 (atan2.f64 im re))) (neg.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))))
	31.2b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
✓	0.3b	(/.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))
	27.6b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	7.6b	(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))))
	29.1b	(/.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (log.f64 base) (sqrt.f64 (atan2.f64 im re))))
▶	0.4b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	0.8b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	31.6b	(/.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)))
	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	29.3b	(.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))))
	33.4b	(/.f64 (/.f64 (neg.f64 (atan2.f64 im re)) (sqrt.f64 (neg.f64 (log.f64 base)))) (sqrt.f64 (neg.f64 (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))))

Compiler

Compiled 3681 to 808 computations (78% 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)))

series496.0ms (8%)

Counts

2 → 44

Calls

2 calls:

458.0ms	(*.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)))
3.0ms	(/.f64 1 (log.f64 base))

simplify95.0ms (1.5%)

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

prune94.0ms (1.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	4	8	12
Picked	1	0	1
Done	0	1	1
Total	97	14	111

Error

0.0b

Counts

111 → 14

Alt Table

Status	Error	Program
	7.6b	(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)))))
	31.2b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	32.3b	(*.f64 (sqrt.f64 (neg.f64 (atan2.f64 im re))) (/.f64 (sqrt.f64 (neg.f64 (atan2.f64 im re))) (neg.f64 (log.f64 base))))
	0.8b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	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))))
▶	0.4b	(*.f64 (atan2.f64 im re) (log1p.f64 (expm1.f64 (/.f64 1 (log.f64 base)))))
✓	0.3b	(/.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))
	31.3b	(.f64 (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 base)))) (sqrt.f64 (/.f64 1 (log.f64 base))))
	0.8b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	31.6b	(/.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)))
	29.3b	(.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))))
	31.4b	(*.f64 (atan2.f64 im re) (exp.f64 (neg.f64 (log.f64 (log.f64 base)))))
	33.4b	(/.f64 (/.f64 (neg.f64 (atan2.f64 im re)) (sqrt.f64 (neg.f64 (log.f64 base)))) (sqrt.f64 (neg.f64 (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))))

Compiler

Compiled 1866 to 889 computations (52.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 1 (log.f64 base))
✓	0.3b	(expm1.f64 (/.f64 1 (log.f64 base)))
✓	0.3b	(log1p.f64 (expm1.f64 (/.f64 1 (log.f64 base))))
✓	0.4b	(*.f64 (atan2.f64 im re) (log1p.f64 (expm1.f64 (/.f64 1 (log.f64 base)))))

series547.0ms (8.9%)

Counts

3 → 60

Calls

3 calls:

466.0ms	(*.f64 (atan2.f64 im re) (log1p.f64 (expm1.f64 (/.f64 1 (log.f64 base)))))
42.0ms	(log1p.f64 (expm1.f64 (/.f64 1 (log.f64 base))))
39.0ms	(expm1.f64 (/.f64 1 (log.f64 base)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 42

Calls

3 calls:

3.0ms	(*.f64 (atan2.f64 im re) (log1p.f64 (expm1.f64 (/.f64 1 (log.f64 base)))))
0.0ms	(expm1.f64 (/.f64 1 (log.f64 base)))
0.0ms	(log1p.f64 (expm1.f64 (/.f64 1 (log.f64 base))))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

525×	`distribute-rgt-in_binary64`
432×	`distribute-lft-in_binary64`
413×	`associate-/l/_binary64`
389×	`associate-/l*_binary64`
291×	`fma-def_binary64`

Counts

102 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	70	1071
1	115	954
2	283	939
3	474	939
4	1378	939
5	4393	939
6	4882	939

prune86.0ms (1.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	2	10	12
Picked	0	1	1
Done	0	1	1
Total	111	13	124

Error

0.0b

Counts

124 → 13

Alt Table

Status	Error	Program
	7.6b	(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)))))
	32.3b	(*.f64 (sqrt.f64 (neg.f64 (atan2.f64 im re))) (/.f64 (sqrt.f64 (neg.f64 (atan2.f64 im re))) (neg.f64 (log.f64 base))))
	0.8b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
	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))))
✓	0.4b	(*.f64 (atan2.f64 im re) (log1p.f64 (expm1.f64 (/.f64 1 (log.f64 base)))))
✓	0.3b	(/.f64 (neg.f64 (atan2.f64 im re)) (neg.f64 (log.f64 base)))
	31.3b	(.f64 (.f64 (atan2.f64 im re) (sqrt.f64 (/.f64 1 (log.f64 base)))) (sqrt.f64 (/.f64 1 (log.f64 base))))
	0.7b	(*.f64 (atan2.f64 im re) (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (/.f64 1 (log.f64 base))) 3))))
	0.8b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	31.6b	(/.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)))
	29.3b	(.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))))
	31.4b	(*.f64 (atan2.f64 im re) (exp.f64 (neg.f64 (log.f64 (log.f64 base)))))
	33.4b	(/.f64 (/.f64 (neg.f64 (atan2.f64 im re)) (sqrt.f64 (neg.f64 (log.f64 base)))) (sqrt.f64 (neg.f64 (log.f64 base))))

Compiler

Compiled 1877 to 1043 computations (44.4% saved)

regimes420.0ms (6.8%)

Accuracy

Total 0.3b remaining (83.9%)

Threshold costs 0.3b (83.9%)

Counts

77 → 1

Compiler

Compiled 6686 to 4336 computations (35.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	17	13
2	23	13
3	27	13
4	28	13
5	28	13

end0.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample1.8s (29.6%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
141.0ms	973×	body	128	nan

Compiler

Compiled 281 to 183 computations (34.9% saved)

Details

analyze665.0ms (10.8%)

sample147.0ms (2.4%)

simplify150.0ms (2.4%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series495.0ms (8%)

rewrite4.0ms (0.1%)

simplify107.0ms (1.7%)

prune42.0ms (0.7%)

localize8.0ms (0.1%)

series465.0ms (7.5%)

rewrite22.0ms (0.4%)

simplify252.0ms (4.1%)

prune124.0ms (2%)

localize7.0ms (0.1%)

series496.0ms (8%)

rewrite13.0ms (0.2%)

simplify95.0ms (1.5%)

prune94.0ms (1.5%)

localize11.0ms (0.2%)

series547.0ms (8.9%)

rewrite5.0ms (0.1%)

simplify73.0ms (1.2%)

prune86.0ms (1.4%)

regimes420.0ms (6.8%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (29.6%)

Profiling