Details

analyze583.0ms (7.8%)

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 (25.3%)

Results

1.6s	8256×	body	128	valid
181.0ms	1011×	body	128	invalid

Compiler

Compiled 95 to 62 computations (34.7% saved)

simplify123.0ms (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
▶	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))
	31.7b	(/.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)))

Status

Error

Program

▶

0.3b

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

31.7b

(/.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 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))

series398.0ms (5.3%)

Counts

1 → 8

Calls

1 calls:

398.0ms

(/.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))

simplify87.0ms (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

prune37.0ms (0.5%)

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

0.0b

Counts

37 → 13

Alt Table

Status	Error	Program
	28.1b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	6.0b	(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))))
	28.1b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (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))))
▶	0.3b	(expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	31.7b	(/.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)))
	1.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	1.7b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	31.1b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	30.6b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	0.7b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	28.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (sqrt.f64 (log.f64 base))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (sqrt.f64 (log.f64 base))))

Compiler

Compiled 937 to 372 computations (60.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))
✓	0.2b	(expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

series1.9s (25.9%)

Counts

2 → 72

Calls

2 calls:

1.5s	(log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))
429.0ms	(expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

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

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Rules

880×	`fma-neg_binary64`
739×	`div-sub_binary64`
725×	`fma-def_binary64`
688×	`sub-neg_binary64`
301×	`neg-mul-1_binary64`

Counts

94 → 36

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	1030
1	59	985
2	89	985
3	165	985
4	271	985
5	1316	985
6	3361	985
7	5514	985

prune57.0ms (0.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	70	14	84

Error

0.0b

Counts

84 → 14

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	30.5b	(expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (sqrt.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
	31.1b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	31.1b	(expm1.f64 (exp.f64 (log.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
	28.1b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	6.0b	(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))))
	28.1b	(*.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (atan2.f64 im re) (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))))
✓	0.3b	(expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	31.7b	(/.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)))
	6.0b	(expm1.f64 (cbrt.f64 (pow.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))
	30.6b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	0.7b	(/.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))))

Compiler

Compiled 1459 to 551 computations (62.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series414.0ms (5.6%)

Counts

2 → 44

Calls

2 calls:

382.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
32.0ms	(/.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)))
2.0ms	(/.f64 1 (log.f64 base))

simplify92.0ms (1.2%)

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

prune86.0ms (1.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	4	8	12
Picked	0	1	1
Done	0	1	1
Total	98	13	111

Error

0.0b

Counts

111 → 13

Alt Table

Status	Error	Program
	28.1b	(*.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (/.f64 1 (sqrt.f64 (log.f64 base))))
✓	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	30.5b	(expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (sqrt.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
	1.2b	(.f64 (.f64 (atan2.f64 im re) (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))))) (/.f64 1 (cbrt.f64 (log.f64 base))))
	31.1b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	28.1b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	6.0b	(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))))
	30.6b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
▶	0.7b	(/.f64 1 (/.f64 (log.f64 base) (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))))
	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))))
✓	0.3b	(expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (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))))

Compiler

Compiled 1789 to 823 computations (54% 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))
✓	0.6b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))

series771.0ms (10.3%)

Counts

2 → 44

Calls

2 calls:

387.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
383.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

rewrite18.0ms (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:

4.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
2.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

simplify127.0ms (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

prune98.0ms (1.3%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	144	14	158

Error

Counts

158 → 14

Alt Table

Status	Error	Program
	28.1b	(*.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (/.f64 1 (sqrt.f64 (log.f64 base))))
✓	0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
	30.5b	(expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base)))) (sqrt.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))))
	1.2b	(.f64 (.f64 (atan2.f64 im re) (/.f64 1 (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))))) (/.f64 1 (cbrt.f64 (log.f64 base))))
	31.1b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
	28.1b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	6.0b	(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))))
	6.1b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 3)))
	30.6b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
✓	0.7b	(/.f64 1 (/.f64 (log.f64 base) (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))))
	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))))
✓	0.3b	(expm1.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (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))))

Compiler

Compiled 2706 to 913 computations (66.3% saved)

regimes456.0ms (6.1%)

Accuracy

Total 0.3b remaining (84.6%)

Threshold costs 0.3b (84.6%)

Counts

93 → 1

Compiler

Compiled 8531 to 5141 computations (39.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	11	9
2	10	9

end160.0ms (2.1%)

Compiler: Compiled 261 to 152 computations (41.8% saved)

Details

analyze583.0ms (7.8%)

sample1.9s (25.3%)

simplify123.0ms (1.7%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series398.0ms (5.3%)

rewrite4.0ms (0.1%)

simplify87.0ms (1.2%)

prune37.0ms (0.5%)

localize8.0ms (0.1%)

series1.9s (25.9%)

rewrite1.0ms (0%)

simplify72.0ms (1%)

prune57.0ms (0.8%)

localize6.0ms (0.1%)

series414.0ms (5.6%)

rewrite14.0ms (0.2%)

simplify92.0ms (1.2%)

prune86.0ms (1.2%)

localize6.0ms (0.1%)

series771.0ms (10.3%)

rewrite18.0ms (0.2%)

simplify127.0ms (1.7%)

prune98.0ms (1.3%)

regimes456.0ms (6.1%)

simplify2.0ms (0%)

end160.0ms (2.1%)

Profiling