Details

analyze2.6s (25%)

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
0%	99.9%	0.1%	7
2.3%	97.5%	0.1%	8
6.2%	93.6%	0.1%	9
9.4%	90.5%	0.1%	10
12%	87.9%	0.1%	11
17.7%	82.1%	0.1%	12
20.1%	79.8%	0.1%	13
21.6%	78.3%	0.1%	14

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample3.8s (36.7%)

Results

1.2s	927×	body	4096	valid
1.1s	5568×	body	128	valid
878.0ms	906×	body	2048	valid
364.0ms	484×	body	1024	valid
145.0ms	235×	body	512	valid
53.0ms	136×	body	256	valid

Compiler

Compiled 53 to 41 computations (22.6% saved)

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

652×	`div-sub_binary64`
554×	`fma-neg_binary64`
550×	`hypot-def_binary64`
431×	`fma-def_binary64`
378×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	36
1	44	25
2	96	25
3	264	25
4	706	25
5	2223	25
6	4175	25
7	4825	25
8	4983	25

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

11.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.1b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
	28.8b	(.f64 180 (/.f64 (atan.f64 (.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))) (PI.f64)))

Status

Error

Program

▶

11.1b

(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))

28.8b

(*.f64 180 (/.f64 (atan.f64 (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))) (PI.f64)))

Compiler

Compiled 132 to 91 computations (31.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
✓	0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))
✓	0.0b	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
✓	0.4b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series216.0ms (2.1%)

Counts

4 → 144

Calls

4 calls:

87.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
58.0ms	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
38.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
31.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64`
71×	`add-sqr-sqrt_binary64`
48×	`add-cube-cbrt_binary64`
37×	`times-frac_binary64`
24×	`prod-diff_binary64`

Counts

4 → 161

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
7.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
7.0ms	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
4.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))

simplify163.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

605×	`fma-def_binary64`
355×	`associate-/l*_binary64`
238×	`times-frac_binary64`
205×	`sub-neg_binary64`
198×	`associate-/r*_binary64`

Counts

305 → 378

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	674	10323
1	1950	9081
2	4971	9081

prune322.0ms (3.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	371	7	378
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	373	7	380

Error

0.3b

Counts

380 → 7

Alt Table

Status	Error	Program
	45.4b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
	50.9b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 1/2 (/.f64 (pow.f64 B 2) A)) B)) (PI.f64)))
	48.4b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
▶	11.1b	(*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)) 180)
	54.5b	(.f64 180 (/.f64 (atan.f64 (fma.f64 1/2 (/.f64 C (/.f64 (.f64 A A) B)) (fma.f64 1/2 (+.f64 (/.f64 B A) (/.f64 (.f64 B (.f64 C C)) (pow.f64 A 3))) (*.f64 (/.f64 (pow.f64 B 3) (pow.f64 A 3)) -1/8)))) (PI.f64)))
	11.1b	(*.f64 180 (/.f64 (atan.f64 (/.f64 1 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))))) (PI.f64)))
	48.6b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))

Compiler

Compiled 13374 to 5253 computations (60.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)) 180)
	0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))
	0.0b	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
	0.4b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series38.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

37.0ms

(*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)) 180)

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-l_binary64`
10×	`times-frac_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 34

Calls

1 calls:

6.0ms

(*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)) 180)

simplify185.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

684×	`fma-def_binary64`
681×	`fma-neg_binary64`
450×	`fabs-mul_binary64`
445×	`associate-*l/_binary64`
445×	`associate-/l*_binary64`

Counts

70 → 61

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	91	2007
1	193	1863
2	448	1863
3	1032	1863
4	2350	1863
5	2755	1863
6	3261	1863
7	3842	1863
8	4451	1863
9	4860	1863
10	4954	1863
11	5104	1863

prune268.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	376	0	376
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	376	7	383

Error

0.3b

Counts

383 → 7

Alt Table

Status	Error	Program
	45.4b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
	50.9b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 1/2 (/.f64 (pow.f64 B 2) A)) B)) (PI.f64)))
	48.4b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
✓	11.1b	(*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)) 180)
	54.5b	(.f64 180 (/.f64 (atan.f64 (fma.f64 1/2 (/.f64 C (/.f64 (.f64 A A) B)) (fma.f64 1/2 (+.f64 (/.f64 B A) (/.f64 (.f64 B (.f64 C C)) (pow.f64 A 3))) (*.f64 (/.f64 (pow.f64 B 3) (pow.f64 A 3)) -1/8)))) (PI.f64)))
▶	11.1b	(*.f64 180 (/.f64 (atan.f64 (/.f64 1 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))))) (PI.f64)))
	48.6b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))

Compiler

Compiled 13329 to 5245 computations (60.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 180 (/.f64 (atan.f64 (/.f64 1 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))))) (PI.f64)))
✓	0.0b	(/.f64 (atan.f64 (/.f64 1 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))))) (PI.f64))
✓	0.1b	(/.f64 1 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))))
	0.4b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series145.0ms (1.4%)

Counts

3 → 108

Calls

3 calls:

78.0ms

(/.f64 1 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))))

37.0ms

(*.f64 180 (/.f64 (atan.f64 (/.f64 1 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))))) (PI.f64)))

29.0ms

(/.f64 (atan.f64 (/.f64 1 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))))) (PI.f64))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

163×	`times-frac_binary64`
144×	`*-un-lft-identity_binary64`
113×	`add-sqr-sqrt_binary64`
84×	`add-cube-cbrt_binary64`
36×	`distribute-lft-out--_binary64`

Counts

3 → 185

Calls

3 calls:

9.0ms

(/.f64 1 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))))

5.0ms

(*.f64 180 (/.f64 (atan.f64 (/.f64 1 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))))) (PI.f64)))

2.0ms

(/.f64 (atan.f64 (/.f64 1 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))))) (PI.f64))

simplify243.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

271×	`fma-neg_binary64`
242×	`fma-def_binary64`
212×	`*-commutative_binary64`
197×	`+-commutative_binary64`
195×	`associate-/l*_binary64`

Counts

293 → 320

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	475	9995
1	1285	8930
2	4430	8896
3	4974	8896
4	4975	8896

prune325.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	456	1	457
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	457	7	464

Error

0.3b

Counts

464 → 7

Alt Table

Status	Error	Program
▶	45.4b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
	50.9b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 1/2 (/.f64 (pow.f64 B 2) A)) B)) (PI.f64)))
	48.4b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
✓	11.1b	(*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)) 180)
	53.7b	(.f64 180 (/.f64 (atan.f64 (fma.f64 1/2 (+.f64 (/.f64 C (/.f64 (.f64 A A) B)) (+.f64 (/.f64 B A) (/.f64 (.f64 C (.f64 C B)) (pow.f64 A 3)))) (*.f64 (/.f64 (pow.f64 B 3) (pow.f64 A 3)) -1/8))) (PI.f64)))
✓	11.1b	(*.f64 180 (/.f64 (atan.f64 (/.f64 1 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))))) (PI.f64)))
	48.6b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))

Compiler

Compiled 16809 to 6980 computations (58.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
✓	4.3b	(+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))
✓	5.1b	(/.f64 C (/.f64 (*.f64 A A) B))
✓	7.5b	(/.f64 (*.f64 A A) B)

series180.0ms (1.7%)

Counts

4 → 132

Calls

4 calls:

59.0ms	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
58.0ms	(/.f64 C (/.f64 (*.f64 A A) B))
50.0ms	(+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))
12.0ms	(/.f64 (*.f64 A A) B)

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
44×	`add-cube-cbrt_binary64`
26×	`fma-def_binary64`

Counts

4 → 149

Calls

4 calls:

18.0ms	(+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))
7.0ms	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))) (PI.f64)))
5.0ms	(/.f64 C (/.f64 (*.f64 A A) B))
3.0ms	(/.f64 (*.f64 A A) B)

simplify164.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

708×	`times-frac_binary64`
548×	`associate-/l*_binary64`
448×	`associate-/l/_binary64`
446×	`associate-/r/_binary64`
381×	`associate-/r*_binary64`

Counts

281 → 218

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	234	4817
1	522	4353
2	1505	4228
3	4573	4225
4	4990	4225
5	4961	4225

prune131.0ms (1.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	214	4	218
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	216	9	225

Error

0.3b

Counts

225 → 9

Alt Table

Status	Error	Program
	48.4b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
✓	11.1b	(*.f64 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)) 180)
	53.7b	(.f64 180 (/.f64 (atan.f64 (fma.f64 1/2 (+.f64 (/.f64 C (/.f64 (.f64 A A) B)) (+.f64 (/.f64 B A) (/.f64 (.f64 C (.f64 C B)) (pow.f64 A 3)))) (*.f64 (/.f64 (pow.f64 B 3) (pow.f64 A 3)) -1/8))) (PI.f64)))
	44.0b	(/.f64 (.f64 180 (atan.f64 (.f64 (*.f64 (/.f64 B A) (+.f64 (/.f64 C A) 1)) 1/2))) (PI.f64))
✓	11.1b	(*.f64 180 (/.f64 (atan.f64 (/.f64 1 (/.f64 B (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))))) (PI.f64)))
	52.4b	(exp.f64 (+.f64 (log.f64 180) (-.f64 (log.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (.f64 A A) B)) (/.f64 B A))))) (log.f64 (PI.f64)))))
	52.1b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (.f64 (sqrt.f64 (+.f64 (/.f64 C (/.f64 (.f64 A A) B)) (/.f64 B A))) (sqrt.f64 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A)))))) (PI.f64)))
	48.6b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
	45.8b	(.f64 (.f64 180 (.f64 (cbrt.f64 (atan.f64 (.f64 (.f64 (/.f64 B A) (+.f64 (/.f64 C A) 1)) 1/2))) (cbrt.f64 (atan.f64 (.f64 (.f64 (/.f64 B A) (+.f64 (/.f64 C A) 1)) 1/2))))) (/.f64 (cbrt.f64 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))))) (PI.f64)))

Compiler

Compiled 6020 to 2585 computations (57.1% saved)

regimes1000.0ms (9.5%)

Accuracy

Total 12.1b remaining (97.3%)

Threshold costs 0b (0%)

Counts

114 → 4

Compiler

Compiled 18228 to 12579 computations (31% saved)

bsearch220.0ms (2.1%)

Steps

Iters	Range	Point
8	-7.294645781180627e-87	-2.8900879796133787e-90	-7.205558733068473e-87
8	-1.235277286249337e-52	-4.2582190071545396e-55	-4.310305532084718e-55
9	-6.024191267419436e+118	-3.229007630929998e+111	-2.783231107200671e+114

Iters

Range

Point

-7.294645781180627e-87

-2.8900879796133787e-90

-7.205558733068473e-87

-1.235277286249337e-52

-4.2582190071545396e-55

-4.310305532084718e-55

-6.024191267419436e+118

-3.229007630929998e+111

-2.783231107200671e+114

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	114
1	65	114
2	77	114
3	85	114
4	88	114
5	87	114

end170.0ms (1.6%)

Compiler: Compiled 391 to 261 computations (33.2% saved)

Details

analyze2.6s (25%)

sample3.8s (36.7%)

simplify66.0ms (0.6%)

prune5.0ms (0%)

localize9.0ms (0.1%)

series216.0ms (2.1%)

rewrite42.0ms (0.4%)

simplify163.0ms (1.6%)

prune322.0ms (3.1%)

localize9.0ms (0.1%)

series38.0ms (0.4%)

rewrite9.0ms (0.1%)

simplify185.0ms (1.8%)

prune268.0ms (2.6%)

localize10.0ms (0.1%)

series145.0ms (1.4%)

rewrite39.0ms (0.4%)

simplify243.0ms (2.3%)

prune325.0ms (3.1%)

localize11.0ms (0.1%)

series180.0ms (1.7%)

rewrite43.0ms (0.4%)

simplify164.0ms (1.6%)

prune131.0ms (1.2%)

regimes1000.0ms (9.5%)

bsearch220.0ms (2.1%)

simplify6.0ms (0.1%)

end170.0ms (1.6%)

Profiling