Details

analyze3.1s (29.6%)

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)

sample3.9s (37.9%)

Results

1.2s	5589×	body	128	valid
1.1s	900×	body	4096	valid
902.0ms	876×	body	2048	valid
365.0ms	485×	body	1024	valid
208.0ms	263×	body	512	valid
70.0ms	143×	body	256	valid

Compiler

Compiled 80 to 62 computations (22.5% saved)

simplify71.0ms (0.7%)

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

12.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	12.4b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
	27.3b	(.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

▶

12.4b

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

27.3b

(*.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)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
✓	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))
✓	0.5b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series223.0ms (2.1%)

Counts

4 → 144

Calls

4 calls:

92.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
62.0ms	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
40.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
29.0ms	(/.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))

simplify172.0ms (1.7%)

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

prune255.0ms (2.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	374	4	378
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	376	4	380

Error

0.1b

Counts

380 → 4

Alt Table

Status	Error	Program
	46.7b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))
	46.6b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
	14.9b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
▶	12.4b	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))

Compiler

Compiled 13204 to 5129 computations (61.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
✓	0.0b	(*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))
✓	0.0b	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
	0.5b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series62.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

44.0ms	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
18.0ms	(*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

5.0ms	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
4.0ms	(*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))

simplify201.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

759×	`div-sub_binary64`
446×	`sub-neg_binary64`
354×	`unswap-sqr_binary64`
332×	`*-commutative_binary64`
298×	`fma-def_binary64`

Counts

115 → 75

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	92	3008
1	189	2775
2	520	2775
3	1776	2775
4	2166	2775
5	2665	2775
6	3523	2775
7	3958	2775
8	4318	2775
9	4960	2775

prune231.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	335	2	337
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	335	6	341

Error

0.1b

Counts

341 → 6

Alt Table

Status	Error	Program
	46.7b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))
	42.3b	(/.f64 (.f64 180 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))))) (PI.f64))
	46.6b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
▶	14.9b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
✓	12.4b	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
	41.8b	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))

Compiler

Compiled 11787 to 5076 computations (56.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)
✓	0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64))
✓	0.0b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
✓	0.7b	(+.f64 A (hypot.f64 B (-.f64 C A)))

series196.0ms (1.9%)

Counts

4 → 80

Calls

4 calls:

80.0ms	(/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)
48.0ms	(+.f64 A (hypot.f64 B (-.f64 C A)))
39.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
28.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
32×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

4 → 124

Calls

4 calls:

7.0ms	(/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)
5.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
4.0ms	(+.f64 A (hypot.f64 B (-.f64 C A)))
2.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64))

simplify123.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-def_binary64`
257×	`associate-/l*_binary64`
208×	`associate--l+_binary64`
206×	`times-frac_binary64`
187×	`associate-r_binary64`

Counts

204 → 265

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	577	7338
1	1737	6586
2	4971	6586

prune189.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	265	0	265
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	265	6	271

Error

0.1b

Counts

271 → 6

Alt Table

Status	Error	Program
	46.7b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))
	42.3b	(/.f64 (.f64 180 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))))) (PI.f64))
	46.6b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
✓	14.9b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
✓	12.4b	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
▶	41.8b	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))

Compiler

Compiled 9501 to 4248 computations (55.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 180 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B))))))
✓	3.6b	(+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))
✓	4.6b	(/.f64 A (/.f64 (*.f64 C C) B))
✓	7.2b	(/.f64 (*.f64 C C) B)

series154.0ms (1.5%)

Counts

4 → 132

Calls

4 calls:

58.0ms	(/.f64 A (/.f64 (*.f64 C C) B))
57.0ms	(+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))
27.0ms	(.f64 180 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B))))))
12.0ms	(/.f64 (*.f64 C C) B)

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 122

Calls

4 calls:

16.0ms	(+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))
5.0ms	(/.f64 A (/.f64 (*.f64 C C) B))
4.0ms	(.f64 180 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B))))))
3.0ms	(/.f64 (*.f64 C C) B)

simplify152.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

665×	`times-frac_binary64`
433×	`associate-/l*_binary64`
425×	`associate-*l/_binary64`
424×	`associate-/r/_binary64`
387×	`associate-/l/_binary64`

Counts

254 → 177

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	192	4048
1	423	3730
2	1227	3551
3	4434	3542
4	4901	3541
5	4965	3541

prune109.0ms (1.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	172	5	177
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	173	10	183

Error

0.0b

Counts

183 → 10

Alt Table

Status	Error	Program
	41.1b	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (*.f64 (+.f64 (/.f64 A (pow.f64 C 2)) (/.f64 1 C)) B)))) (PI.f64))
	46.7b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))
	42.3b	(/.f64 (.f64 180 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))))) (PI.f64))
	46.6b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
✓	14.9b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))
✓	12.4b	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
	41.9b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 180 (atan.f64 (.f64 (.f64 (/.f64 B C) (+.f64 (/.f64 A C) 1)) -1/2)))) (cbrt.f64 (.f64 180 (atan.f64 (.f64 (.f64 (/.f64 B C) (+.f64 (/.f64 A C) 1)) -1/2))))) (cbrt.f64 (.f64 180 (atan.f64 (.f64 (*.f64 (/.f64 B C) (+.f64 (/.f64 A C) 1)) -1/2))))) (PI.f64))
	51.1b	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (/.f64 (fma.f64 C A (*.f64 C C)) (/.f64 (pow.f64 C 3) B))))) (PI.f64))
	54.3b	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (fma.f64 (/.f64 (sqrt.f64 B) 1) (/.f64 (sqrt.f64 B) C) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))
	41.4b	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (fma.f64 (/.f64 (.f64 (cbrt.f64 B) (cbrt.f64 B)) 1) (/.f64 (cbrt.f64 B) C) (/.f64 A (/.f64 (.f64 C C) B)))))) (PI.f64))

Compiler

Compiled 4661 to 2074 computations (55.5% saved)

regimes824.0ms (7.9%)

Accuracy

Total 12.1b remaining (97.6%)

Threshold costs 0b (0%)

Counts

99 → 2

Compiler

Compiled 14553 to 10829 computations (25.6% saved)

bsearch79.0ms (0.8%)

Steps

Iters	Range		Point
7	-1.5716448250812538e+137	-3.0966923369970064e+135	-4.693515796693692e+135

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	47
1	32	47
2	43	47
3	51	47
4	55	47
5	56	47
6	56	47

end169.0ms (1.6%)

Compiler: Compiled 301 to 214 computations (28.9% saved)

Details

analyze3.1s (29.6%)

sample3.9s (37.9%)

simplify71.0ms (0.7%)

prune5.0ms (0%)

localize10.0ms (0.1%)

series223.0ms (2.1%)

rewrite42.0ms (0.4%)

simplify172.0ms (1.7%)

prune255.0ms (2.4%)

localize9.0ms (0.1%)

series62.0ms (0.6%)

rewrite11.0ms (0.1%)

simplify201.0ms (1.9%)

prune231.0ms (2.2%)

localize11.0ms (0.1%)

series196.0ms (1.9%)

rewrite27.0ms (0.3%)

simplify123.0ms (1.2%)

prune189.0ms (1.8%)

localize11.0ms (0.1%)

series154.0ms (1.5%)

rewrite35.0ms (0.3%)

simplify152.0ms (1.5%)

prune109.0ms (1.1%)

regimes824.0ms (7.9%)

bsearch79.0ms (0.8%)

simplify4.0ms (0%)

end169.0ms (1.6%)

Profiling