Details

analyze674.0ms (9.5%)

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)

sample50.0ms (0.7%)

Algorithm

1×

intervals

Results

33.0ms	256×	body	128	valid
3.0ms	25×	body	128	nan

Compiler

Compiled 66 to 44 computations (33.3% saved)

simplify130.0ms (1.8%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	29.6b	(/.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)))
▶	0.2b	(/.f64 (atan2.f64 im re) (log.f64 base))

Status

Error

Program

29.6b

(/.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)))

▶

0.2b

(/.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
✓	0.2b	(/.f64 (atan2.f64 im re) (log.f64 base))

series406.0ms (5.7%)

Counts

1 → 8

Calls

1 calls:

406.0ms

(/.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 (1.2%)

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

prune35.0ms (0.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	24	11	35
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	25	12	37

Error

0.0b

Counts

37 → 12

Alt Table

Status	Error	Program
	29.6b	(/.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)))
	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))))
	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))))
	30.6b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	27.9b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
▶	0.2b	(pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 1)
	0.4b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	1.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	30.3b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))
	1.6b	(.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))))
	1.6b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	27.2b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))

Compiler

Compiled 921 to 354 computations (61.6% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

prune35.0ms (0.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	35	12	47

Error

0.0b

Counts

47 → 12

Alt Table

Status	Error	Program
	29.6b	(/.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)))
	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))))
	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))))
	30.6b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	27.9b	(exp.f64 (log.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))
✓	0.2b	(pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 1)
▶	0.4b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	1.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	30.3b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))
	1.6b	(.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))))
	1.6b	(.f64 (.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re))) (/.f64 (cbrt.f64 (atan2.f64 im re)) (log.f64 base)))
	27.2b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))

Compiler

Compiled 980 to 416 computations (57.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series845.0ms (11.9%)

Counts

2 → 44

Calls

2 calls:

437.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
407.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

rewrite17.0ms (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:

5.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
3.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

simplify147.0ms (2.1%)

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

prune113.0ms (1.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	136	7	143
Fresh	4	6	10
Picked	1	0	1
Done	0	1	1
Total	141	14	155

Error

0.0b

Counts

155 → 14

Alt Table

Status	Error	Program
	29.6b	(/.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)))
	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))))
	30.7b	(/.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (sqrt.f64 (log.f64 base)) (atan2.f64 im re)))
▶	0.4b	(expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))))
	8.4b	(/.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)))))
	30.3b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))
	30.0b	(/.f64 (/.f64 1 (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
	8.4b	(/.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)))))
	30.6b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	1.7b	(/.f64 1 (/.f64 (/.f64 (log.f64 base) (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))) (cbrt.f64 (atan2.f64 im re))))
✓	0.2b	(pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 1)
	1.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	10.6b	(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (atan2.f64 im re)))))
	27.2b	(*.f64 (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) (sqrt.f64 (/.f64 (atan2.f64 im re) (log.f64 base))))

Compiler

Compiled 2956 to 1052 computations (64.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))))
✓	0.1b	(log1p.f64 (/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re))))
	0.3b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
	0.3b	(/.f64 (log.f64 base) (atan2.f64 im re))

series2.1s (29.2%)

Counts

2 → 72

Calls

2 calls:

1.6s	(log1p.f64 (/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re))))
428.0ms	(expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))))

rewrite2.0ms (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	(log1p.f64 (/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re))))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))))

simplify107.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-def_binary64`
539×	`neg-mul-1_binary64`
459×	`fma-neg_binary64`
403×	`neg-sub0_binary64`
354×	`unsub-neg_binary64`

Counts

94 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	1099
1	66	1038
2	116	985
3	249	985
4	793	985
5	2532	985
6	3312	985
7	4698	985
8	4883	985

prune156.0ms (2.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	182	3	185
Fresh	2	10	12
Picked	0	1	1
Done	0	1	1
Total	184	15	199

Error

0.0b

Counts

199 → 15

Alt Table

Status	Error	Program
	30.7b	(/.f64 (/.f64 1 (sqrt.f64 (log.f64 base))) (/.f64 (sqrt.f64 (log.f64 base)) (atan2.f64 im re)))
✓	0.4b	(expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))))
	1.6b	(expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re))))) (cbrt.f64 (log1p.f64 (/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))))) (cbrt.f64 (log1p.f64 (/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))))))
✓	0.2b	(pow.f64 (/.f64 (atan2.f64 im re) (log.f64 base)) 1)
	8.4b	(/.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)))))
	30.3b	(*.f64 (sqrt.f64 (atan2.f64 im re)) (/.f64 (sqrt.f64 (atan2.f64 im re)) (log.f64 base)))
	8.4b	(expm1.f64 (log1p.f64 (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (log.f64 base) (atan2.f64 im re)) 3)))))
	27.2b	(*.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))))
	30.6b	(/.f64 (/.f64 (atan2.f64 im re) (sqrt.f64 (log.f64 base))) (sqrt.f64 (log.f64 base)))
	1.7b	(/.f64 1 (/.f64 (/.f64 (log.f64 base) (*.f64 (cbrt.f64 (atan2.f64 im re)) (cbrt.f64 (atan2.f64 im re)))) (cbrt.f64 (atan2.f64 im re))))
	8.3b	(expm1.f64 (cbrt.f64 (pow.f64 (log1p.f64 (/.f64 (atan2.f64 im re) (log.f64 base))) 3)))
	1.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (/.f64 (atan2.f64 im re) (cbrt.f64 (log.f64 base))))
	30.0b	(/.f64 (/.f64 1 (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re)))) (sqrt.f64 (/.f64 (log.f64 base) (atan2.f64 im re))))
	10.6b	(/.f64 1 (log.f64 (pow.f64 base (/.f64 1 (atan2.f64 im re)))))

Compiler

Compiled 3593 to 1440 computations (59.9% saved)

regimes499.0ms (7.1%)

Accuracy

Total 0.3b remaining (84.5%)

Threshold costs 0.3b (84.5%)

Counts

82 → 1

Compiler

Compiled 6991 to 4546 computations (35% 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

end0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample1.7s (23.5%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
115.0ms	999×	body	128	nan

Compiler

Compiled 322 to 193 computations (40.1% saved)

Details

analyze674.0ms (9.5%)

sample50.0ms (0.7%)

simplify130.0ms (1.8%)

prune5.0ms (0.1%)

localize5.0ms (0.1%)

series406.0ms (5.7%)

rewrite5.0ms (0.1%)

simplify87.0ms (1.2%)

prune35.0ms (0.5%)

localize8.0ms (0.1%)

prune35.0ms (0.5%)

localize7.0ms (0.1%)

series845.0ms (11.9%)

rewrite17.0ms (0.2%)

simplify147.0ms (2.1%)

prune113.0ms (1.6%)

localize12.0ms (0.2%)

series2.1s (29.2%)

rewrite2.0ms (0%)

simplify107.0ms (1.5%)

prune156.0ms (2.2%)

regimes499.0ms (7.1%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.7s (23.5%)

Profiling