Details

analyze361.0ms (4.2%)

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
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
87.4%	12.5%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
93.6%	6.2%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 27 to 21 computations (22.2% saved)

sample3.7s (43.4%)

Results

1.1s	881×	body	4096	valid
1.1s	5634×	body	128	valid
876.0ms	893×	body	2048	valid
349.0ms	476×	body	1024	valid
143.0ms	252×	body	512	valid
45.0ms	120×	body	256	valid

Compiler

Compiled 80 to 62 computations (22.5% saved)

simplify66.0ms (0.8%)

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 (0.1%)

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

13.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.6b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
	30.9b	(.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

▶

13.6b

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

30.9b

(*.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)

localize11.0ms (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)
✓	1.2b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series198.0ms (2.3%)

Counts

4 → 144

Calls

4 calls:

75.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
59.0ms	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
36.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
27.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))

rewrite49.0ms (0.6%)

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:

11.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64)))
10.0ms	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))
9.0ms	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
4.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)) (PI.f64))

simplify153.0ms (1.8%)

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

prune340.0ms (4%)

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

0.2b

Counts

380 → 7

Alt Table

Status	Error	Program
	48.4b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))
	49.5b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
	49.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 1/2 (/.f64 (pow.f64 B 2) A)) B)) (PI.f64)))
	13.6b	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
	46.7b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
▶	13.6b	(.f64 180 (/.f64 (atan.f64 (.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64)))
	52.3b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (fma.f64 (sqrt.f64 (-.f64 C A)) (sqrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) B)) (PI.f64)))

Compiler

Compiled 13326 to 5215 computations (60.9% saved)

localize11.0ms (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))) (/.f64 1 B))) (PI.f64)))
✓	0.0b	(/.f64 (atan.f64 (*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64))
✓	0.2b	(*.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))
	1.2b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series143.0ms (1.7%)

Counts

3 → 108

Calls

3 calls:

77.0ms

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

38.0ms

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

28.0ms

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

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
30×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64`
26×	`associate-r_binary64`

Counts

3 → 108

Calls

3 calls:

11.0ms

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

9.0ms

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

4.0ms

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

simplify146.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

384×	`sub-neg_binary64`
271×	`fma-neg_binary64`
243×	`fma-def_binary64`
211×	`*-commutative_binary64`
197×	`+-commutative_binary64`

Counts

216 → 250

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	434	6928
1	1232	6342
2	4361	6308
3	5198	6308

prune309.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	386	1	387
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	387	7	394

Error

0.2b

Counts

394 → 7

Alt Table

Status	Error	Program
	48.4b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))
	49.5b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (pow.f64 B 2) C)) B)) (PI.f64)))
	49.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 1/2 (/.f64 (pow.f64 B 2) A)) B)) (PI.f64)))
▶	13.6b	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
	46.7b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
	52.3b	(.f64 180 (/.f64 (atan.f64 (.f64 (fma.f64 (sqrt.f64 (-.f64 C A)) (sqrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) (/.f64 1 B))) (PI.f64)))
✓	13.6b	(.f64 180 (/.f64 (atan.f64 (.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64)))

Compiler

Compiled 14032 to 6352 computations (54.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))
	0.0b	(/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)
	1.2b	(-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A)))

series51.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

37.0ms	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
13.0ms	(*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B)))

rewrite13.0ms (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:

6.0ms	(/.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)))

simplify183.0ms (2.1%)

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

prune276.0ms (3.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	334	3	337
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	335	9	344

Error

0.1b

Counts

344 → 9

Alt Table

Status	Error	Program
	49.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 1/2 (/.f64 (pow.f64 B 2) A)) B)) (PI.f64)))
▶	43.0b	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))
✓	13.6b	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
	46.7b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/2 (/.f64 B C))) (PI.f64)))
✓	13.6b	(.f64 180 (/.f64 (atan.f64 (.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64)))
	43.9b	(/.f64 (.f64 180 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))))) (PI.f64))
	48.4b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))
	52.3b	(.f64 180 (/.f64 (atan.f64 (.f64 (fma.f64 (sqrt.f64 (-.f64 C A)) (sqrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) (/.f64 1 B))) (PI.f64)))
	49.5b	(/.f64 (.f64 180 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (*.f64 B B) C)) B))) (PI.f64))

Compiler

Compiled 11892 to 5150 computations (56.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))
✓	4.1b	(+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))
✓	5.1b	(/.f64 A (/.f64 (*.f64 C C) B))
✓	6.7b	(/.f64 (*.f64 C C) B)

series189.0ms (2.2%)

Counts

4 → 132

Calls

4 calls:

64.0ms	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))
57.0ms	(/.f64 A (/.f64 (*.f64 C C) B))
56.0ms	(+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))
12.0ms	(/.f64 (*.f64 C C) B)

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
23×	`add-cbrt-cube_binary64`

Counts

4 → 125

Calls

4 calls:

18.0ms	(+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))
5.0ms	(/.f64 (*.f64 C C) B)
5.0ms	(/.f64 A (/.f64 (*.f64 C C) B))
4.0ms	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))

simplify133.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

913×	`times-frac_binary64`
714×	`associate-/l*_binary64`
498×	`associate-/l/_binary64`
492×	`associate-/r/_binary64`
192×	`fma-neg_binary64`

Counts

257 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	4422
1	480	3981
2	1514	3876
3	4962	3876
4	5072	3876

prune125.0ms (1.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	180	3	183
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	180	12	192

Error

0.1b

Counts

192 → 12

Alt Table

Status	Error	Program
	42.3b	(.f64 (.f64 (cbrt.f64 (.f64 180 (/.f64 (atan.f64 (.f64 (.f64 (/.f64 B C) (+.f64 (/.f64 A C) 1)) -1/2)) (PI.f64)))) (cbrt.f64 (.f64 180 (/.f64 (atan.f64 (.f64 (.f64 (/.f64 B C) (+.f64 (/.f64 A C) 1)) -1/2)) (PI.f64))))) (cbrt.f64 (.f64 180 (/.f64 (atan.f64 (.f64 (*.f64 (/.f64 B C) (+.f64 (/.f64 A C) 1)) -1/2)) (PI.f64)))))
	43.0b	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (fma.f64 (/.f64 (.f64 (cbrt.f64 B) (cbrt.f64 B)) (.f64 (cbrt.f64 C) (cbrt.f64 C))) (/.f64 (cbrt.f64 B) (cbrt.f64 C)) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))
	52.3b	(.f64 180 (/.f64 (atan.f64 (.f64 (fma.f64 (sqrt.f64 (-.f64 C A)) (sqrt.f64 (-.f64 C A)) (neg.f64 (hypot.f64 B (-.f64 C A)))) (/.f64 1 B))) (PI.f64)))
	49.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (.f64 1/2 (/.f64 (pow.f64 B 2) A)) B)) (PI.f64)))
✓	43.0b	(/.f64 (.f64 180 (atan.f64 (.f64 -1/2 (+.f64 (/.f64 B C) (/.f64 A (/.f64 (*.f64 C C) B)))))) (PI.f64))
✓	13.6b	(/.f64 (*.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) B))) (PI.f64))
	42.9b	(/.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 C))) (PI.f64)))
✓	13.6b	(.f64 180 (/.f64 (atan.f64 (.f64 (-.f64 (-.f64 C A) (hypot.f64 B (-.f64 C A))) (/.f64 1 B))) (PI.f64)))
	43.9b	(/.f64 (.f64 180 (atan.f64 (.f64 1/2 (+.f64 (/.f64 C (/.f64 (*.f64 A A) B)) (/.f64 B A))))) (PI.f64))
	48.4b	(.f64 180 (/.f64 (atan.f64 (.f64 1/2 (/.f64 B A))) (PI.f64)))
	49.5b	(/.f64 (.f64 180 (atan.f64 (/.f64 (.f64 -1/2 (/.f64 (*.f64 B B) C)) B))) (PI.f64))

Compiler

Compiled 4773 to 2108 computations (55.8% saved)

regimes1.8s (20.7%)

Accuracy

Total 10.6b remaining (97.1%)

Threshold costs 0b (0%)

Counts

181 → 3

Compiler

Compiled 33012 to 21077 computations (36.2% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
9×	`+-commutative_binary64`
8×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	133
1	58	133
2	71	133
3	79	133
4	83	133
5	82	133

end209.0ms (2.4%)

Compiler: Compiled 458 to 302 computations (34.1% saved)

Details

analyze361.0ms (4.2%)

sample3.7s (43.4%)

simplify66.0ms (0.8%)

prune5.0ms (0.1%)

localize11.0ms (0.1%)

series198.0ms (2.3%)

rewrite49.0ms (0.6%)

simplify153.0ms (1.8%)

prune340.0ms (4%)

localize11.0ms (0.1%)

series143.0ms (1.7%)

rewrite32.0ms (0.4%)

simplify146.0ms (1.7%)

prune309.0ms (3.6%)

localize10.0ms (0.1%)

series51.0ms (0.6%)

rewrite13.0ms (0.1%)

simplify183.0ms (2.1%)

prune276.0ms (3.2%)

localize11.0ms (0.1%)

series189.0ms (2.2%)

rewrite39.0ms (0.5%)

simplify133.0ms (1.5%)

prune125.0ms (1.5%)

regimes1.8s (20.7%)

bsearch8.0ms (0.1%)

simplify6.0ms (0.1%)

end209.0ms (2.4%)

Profiling