Details

analyze2.1s (10.6%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	62.4%	12.6%	8
31.2%	56.2%	12.6%	9
34.3%	53%	12.6%	10
42.9%	44.5%	12.6%	11
46.8%	40.6%	12.6%	12
47.8%	39.6%	12.6%	13
52.6%	34.8%	12.6%	14

Compiler

Compiled 25 to 20 computations (20% saved)

sample7.9s (40.4%)

Results

2.3s	1683×	body	1024	valid
2.0s	1423×	body	1024	invalid
1.2s	5158×	body	128	valid
711.0ms	796×	body	512	valid
704.0ms	761×	body	512	invalid
384.0ms	184×	body	2048	valid
227.0ms	435×	body	256	valid
182.0ms	327×	body	256	invalid
156.0ms	666×	body	128	invalid

Compiler

Compiled 74 to 59 computations (20.3% saved)

simplify39.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

648×	`rules-4_binary64`
514×	`rules-33_binary64`
297×	`rules-1_binary64`
286×	`rules-23-rev_binary64`
244×	`fma-def_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	34
1	26	34
2	53	34
3	141	34
4	634	34
5	4272	34
6	5020	34

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

21.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))

Compiler

Compiled 72 to 57 computations (20.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)
✓	0.3b	(*.f64 (PI.f64) (/.f64 angle 180))
✓	25.8b	(cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))
✓	25.9b	(sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))

series33.0ms (0.2%)

Counts

4 → 60

Calls

4 calls:

22.0ms	(pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)
5.0ms	(*.f64 (PI.f64) (/.f64 angle 180))
3.0ms	(sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))
3.0ms	(cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))

rewrite86.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

615×	`prod-diff_binary64`
210×	`expm1-udef_binary64`
210×	`log1p-udef_binary64`
188×	`egg-rr`
119×	`add-sqr-sqrt_binary64`

Counts

4 → 188

Calls

4 calls:

82.0ms	(pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)
82.0ms	(*.f64 (PI.f64) (/.f64 angle 180))
82.0ms	(cos.f64 (*.f64 (PI.f64) (/.f64 angle 180)))
82.0ms	(sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	44
1	281	44
2	3293	44
3	5059	44
0	0	0
1	0	0

simplify63.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

490×	`rules-11_binary64`
474×	`fma-neg_binary64`
352×	`rules-6_binary64`
331×	`rules-20_binary64`
287×	`fma-def_binary64`

Counts

248 → 214

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1058
1	245	1058
2	1043	1046
3	4926	1040
4	4951	1040

prune847.0ms (4.4%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	254	32	286
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	255	32	287

Error

19.3b

Counts

287 → 32

Alt Table

Status	Error	Program
	40.6b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 angle 180)) 3) 1/3))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cbrt.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 3))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (.f64 (cbrt.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (cbrt.f64 (/.f64 angle 180)) (.f64 (PI.f64) (pow.f64 (cbrt.f64 (/.f64 angle 180)) 2)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	36.5b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (-.f64 (+.f64 (.f64 1/765275040000000 (.f64 (pow.f64 angle 6) (.f64 (pow.f64 (PI.f64) 6) (pow.f64 b 2)))) (.f64 1/32400 (.f64 (pow.f64 angle 2) (.f64 (pow.f64 (PI.f64) 2) (pow.f64 b 2))))) (+.f64 (.f64 1/3149280000 (.f64 (pow.f64 angle 4) (.f64 (pow.f64 (PI.f64) 4) (pow.f64 b 2)))) (.f64 1/347128758144000000000 (.f64 (pow.f64 angle 8) (.f64 (pow.f64 (PI.f64) 8) (pow.f64 b 2)))))))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 angle) 2) (/.f64 (cbrt.f64 angle) (/.f64 180 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	25.9b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (expm1.f64 (log1p.f64 (.f64 (PI.f64) (/.f64 angle 180)))))) 2))
	21.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 angle) 2) (/.f64 (cbrt.f64 angle) (/.f64 180 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (.f64 (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (pow.f64 (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b)) (.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b)) 2))))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2) (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 0))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (/.f64 (.f64 (PI.f64) angle) 180))) 2))
	21.4b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2))
	28.0b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64)))) 2)))
	21.4b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2) (cbrt.f64 (*.f64 (PI.f64) (/.f64 angle 180))) 0))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (cbrt.f64 (PI.f64)) (.f64 (/.f64 angle 180) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	22.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (.f64 b (.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))))
	21.5b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (cbrt.f64 (PI.f64)) (.f64 (/.f64 angle 180) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2))
▶	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	24.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) (.f64 (.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) b) b)))
	44.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2))) 2))
	36.7b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 1))) 2))
	26.9b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) 2))) 1))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 3))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (sqrt.f64 angle) (/.f64 (sqrt.f64 angle) (/.f64 180 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (/.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (/.f64 1 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b))))
	34.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 angle 180)) 3) 1/3))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	28.6b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b)) 2) (cbrt.f64 (pow.f64 (.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) b) 4))))
	21.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 angle 180)) 2) (.f64 (cbrt.f64 (/.f64 angle 180)) (PI.f64)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 3) (+.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2) (+.f64 0 (.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 0))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (sqrt.f64 (PI.f64)) (.f64 (/.f64 angle 180) (sqrt.f64 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))

Compiler

Compiled 11670 to 8679 computations (25.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))))
	0.3b	(pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2)
	0.3b	(*.f64 (PI.f64) (/.f64 angle 180))
	25.9b	(sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))

series13.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

13.0ms

(*.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))

rewrite57.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

871×	`expm1-log1p-u_binary64`
570×	`prod-diff_binary64`
92×	`add-sqr-sqrt_binary64`
85×	`log1p-expm1-u_binary64`
84×	`add-cbrt-cube_binary64`

Counts

1 → 63

Calls

1 calls:

55.0ms

(*.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	208	13
2	2592	13
3	5230	13
0	0	0
1	0	0

simplify44.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

721×	`rules-13_binary64`
489×	`rules-4_binary64`
376×	`rules-15-rev_binary64`
216×	`rules-11_binary64`
196×	`rules-6_binary64`

Counts

87 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	412
1	116	412
2	444	406
3	3265	406
4	6008	406

prune824.0ms (4.2%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	231	16	247
Fresh	15	16	31
Picked	1	0	1
Done	0	0	0
Total	247	32	279

Error

19.3b

Counts

279 → 32

Alt Table

Status	Error	Program
	40.6b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 angle 180)) 3) 1/3))) 2))
	26.7b	(+.f64 (pow.f64 (.f64 a 1) 2) (-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) b) 2))) 1))
	21.2b	(+.f64 (pow.f64 (.f64 a (cbrt.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 3))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	26.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (cbrt.f64 (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 3)) 2))
	22.1b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 b (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b))))
	21.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2) (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 0))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (cbrt.f64 (/.f64 angle 180)) (.f64 (PI.f64) (pow.f64 (cbrt.f64 (/.f64 angle 180)) 2)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	25.6b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (expm1.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) 2))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b)) 2) (.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b)) (.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) b))))
	21.2b	(+.f64 (pow.f64 (.f64 a (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 3) (+.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2) (+.f64 0 (.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 0))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	36.4b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 1))) 2))
	36.5b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (-.f64 (+.f64 (.f64 1/765275040000000 (.f64 (pow.f64 angle 6) (.f64 (pow.f64 (PI.f64) 6) (pow.f64 b 2)))) (.f64 1/32400 (.f64 (pow.f64 angle 2) (.f64 (pow.f64 (PI.f64) 2) (pow.f64 b 2))))) (+.f64 (.f64 1/3149280000 (.f64 (pow.f64 angle 4) (.f64 (pow.f64 (PI.f64) 4) (pow.f64 b 2)))) (.f64 1/347128758144000000000 (.f64 (pow.f64 angle 8) (.f64 (pow.f64 (PI.f64) 8) (pow.f64 b 2)))))))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 angle) 2) (/.f64 (cbrt.f64 angle) (/.f64 180 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	28.4b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) 4)) (pow.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b)) 2)))
	21.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 angle) 2) (/.f64 (cbrt.f64 angle) (/.f64 180 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64)))))) 2))
▶	20.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (/.f64 1 (.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) b))))
	21.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (pow.f64 (cbrt.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) 3) 2))
	27.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (*.f64 angle (PI.f64)))) 2)))
	21.2b	(+.f64 (pow.f64 (.f64 a (.f64 (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (pow.f64 (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2) (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 0))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.3b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (cbrt.f64 (PI.f64)) (.f64 (/.f64 angle 180) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64)))))) 2))
	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (/.f64 (*.f64 (PI.f64) angle) 180))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (cbrt.f64 (PI.f64)) (.f64 (/.f64 angle 180) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64)))))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 3))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (sqrt.f64 angle) (/.f64 (sqrt.f64 angle) (/.f64 180 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	43.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 angle 180))) 2))) 2))
	34.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 angle 180)) 3) 1/3))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	24.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) (.f64 b (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b))))
	21.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 angle 180)) 2) (.f64 (cbrt.f64 (/.f64 angle 180)) (PI.f64)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (sqrt.f64 (PI.f64)) (.f64 (/.f64 angle 180) (sqrt.f64 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))

Compiler

Compiled 9380 to 7140 computations (23.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b))
✓	0.3b	(.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b)
	0.3b	(*.f64 (PI.f64) (/.f64 angle 180))
	25.9b	(sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))

series51.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

37.0ms	(/.f64 1 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b))
14.0ms	(.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b)

rewrite77.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

850×	`fma-neg_binary64`
591×	`prod-diff_binary64`
190×	`expm1-udef_binary64`
190×	`log1p-udef_binary64`
140×	`egg-rr`

Counts

2 → 140

Calls

2 calls:

73.0ms	(/.f64 1 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b))
73.0ms	(.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	249	29
2	3016	29
3	5399	29
0	0	0
1	0	0

simplify38.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

664×	`rules-4_binary64`
444×	`fma-def_binary64`
288×	`rules-6_binary64`
280×	`rules-13_binary64`
273×	`rules-20_binary64`

Counts

188 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	60	860
1	197	860
2	842	854
3	5271	854

prune1.9s (9.5%)

Pruning

35 alts after pruning (35 fresh and 0 done)

	Pruned	Kept	Total
New	479	10	489
Fresh	6	25	31
Picked	1	0	1
Done	0	0	0
Total	486	35	521

Error

18.7b

Counts

521 → 35

Alt Table

Status	Error	Program
	21.4b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (/.f64 1 (.f64 (sin.f64 (+.f64 (fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 angle 180)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64))))) b))))
	26.7b	(+.f64 (pow.f64 (.f64 a 1) 2) (-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) b) 2))) 1))
	40.6b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 angle 180)) 3) 1/3))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cbrt.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 3))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	34.5b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (log.f64 (exp.f64 (/.f64 1 (.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) b))))))
	26.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (cbrt.f64 (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 3)) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2) (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 0))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (cbrt.f64 (/.f64 angle 180)) (.f64 (PI.f64) (pow.f64 (cbrt.f64 (/.f64 angle 180)) 2)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2) (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 0)) b) (/.f64 1 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b))))
	25.6b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (expm1.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 angle 180)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 3) (+.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2) (+.f64 0 (.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 0))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 angle) 2) (/.f64 (cbrt.f64 angle) (/.f64 180 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	26.1b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (expm1.f64 (log1p.f64 (.f64 (PI.f64) (/.f64 angle 180))))) b) (/.f64 1 (.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) b))))
	21.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (pow.f64 (cbrt.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) 3) 2))
	21.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 angle) 2) (/.f64 (cbrt.f64 angle) (/.f64 180 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (.f64 (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (pow.f64 (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	25.5b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 1/180 (.f64 angle (.f64 (PI.f64) b))) (/.f64 1 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b))))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2) (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 0))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.3b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (cbrt.f64 (PI.f64)) (.f64 (/.f64 angle 180) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64)))))) 2))
▶	21.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (/.f64 (*.f64 (PI.f64) angle) 180))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (cbrt.f64 (PI.f64)) (.f64 (/.f64 angle 180) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64)))))) 2))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (sqrt.f64 angle) (/.f64 (sqrt.f64 angle) (/.f64 180 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 angle) 2) (/.f64 (cbrt.f64 angle) (/.f64 180 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64))))) b) (/.f64 1 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b))))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 3))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	43.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 angle 180))) 2))) 2))
	22.1b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (fma.f64 1/1080 (/.f64 (.f64 angle (PI.f64)) b) (fma.f64 7/2099520000 (/.f64 (.f64 (pow.f64 angle 3) (pow.f64 (PI.f64) 3)) b) (/.f64 180 (.f64 angle (*.f64 (PI.f64) b)))))))
	34.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 angle 180)) 3) 1/3))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	22.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (/.f64 1 (.f64 (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 angle 180)) 2) (.f64 (cbrt.f64 (/.f64 angle 180)) (PI.f64)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64))))) b))))
	24.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) (.f64 b (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b))))
	21.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 angle 180)) 2) (.f64 (cbrt.f64 (/.f64 angle 180)) (PI.f64)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (/.f64 1 (.f64 (sin.f64 (+.f64 (fma.f64 (cbrt.f64 (PI.f64)) (.f64 (/.f64 angle 180) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64))))) b))))
	22.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (/.f64 1 (.f64 (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64))))) b))))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (sqrt.f64 (PI.f64)) (.f64 (/.f64 angle 180) (sqrt.f64 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))

Compiler

Compiled 20329 to 15006 computations (26.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 (PI.f64) angle) 180)
✓	0.3b	(.f64 b (sin.f64 (/.f64 (.f64 (PI.f64) angle) 180)))
✓	0.3b	(pow.f64 (.f64 b (sin.f64 (/.f64 (.f64 (PI.f64) angle) 180))) 2)
✓	25.9b	(sin.f64 (/.f64 (*.f64 (PI.f64) angle) 180))

series43.0ms (0.2%)

Counts

4 → 72

Calls

4 calls:

22.0ms	(pow.f64 (.f64 b (sin.f64 (/.f64 (.f64 (PI.f64) angle) 180))) 2)
16.0ms	(.f64 b (sin.f64 (/.f64 (.f64 (PI.f64) angle) 180)))
3.0ms	(sin.f64 (/.f64 (*.f64 (PI.f64) angle) 180))
3.0ms	(/.f64 (*.f64 (PI.f64) angle) 180)

rewrite94.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

830×	`fma-neg_binary64`
377×	`prod-diff_binary64`
262×	`egg-rr`
190×	`expm1-udef_binary64`
190×	`log1p-udef_binary64`

Counts

4 → 262

Calls

4 calls:

88.0ms	(/.f64 (*.f64 (PI.f64) angle) 180)
88.0ms	(.f64 b (sin.f64 (/.f64 (.f64 (PI.f64) angle) 180)))
88.0ms	(pow.f64 (.f64 b (sin.f64 (/.f64 (.f64 (PI.f64) angle) 180))) 2)
88.0ms	(sin.f64 (/.f64 (*.f64 (PI.f64) angle) 180))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	47
1	257	47
2	2971	47
3	4926	47
0	0	0
1	0	0

simplify49.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

586×	`rules-11_binary64`
531×	`fma-neg_binary64`
481×	`rules-6_binary64`
395×	`rules-20_binary64`
368×	`fma-def_binary64`

Counts

334 → 287

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	1296
1	269	1296
2	1168	1275
3	5360	1275

prune1.0s (5.2%)

Pruning

37 alts after pruning (37 fresh and 0 done)

	Pruned	Kept	Total
New	281	6	287
Fresh	3	31	34
Picked	1	0	1
Done	0	0	0
Total	285	37	322

Error

18.7b

Counts

322 → 37

Alt Table

Status	Error	Program
	21.4b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (/.f64 1 (.f64 (sin.f64 (+.f64 (fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 angle 180)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64))))) b))))
	26.7b	(+.f64 (pow.f64 (.f64 a 1) 2) (-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) b) 2))) 1))
	40.6b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 angle 180)) 3) 1/3))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cbrt.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 3))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	26.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 (/.f64 (*.f64 (PI.f64) angle) 180)) b) 3)) 2))
	21.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 angle 180)) 2) (.f64 (cbrt.f64 (/.f64 angle 180)) (PI.f64)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2) (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 0))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (cbrt.f64 (/.f64 angle 180)) (.f64 (PI.f64) (pow.f64 (cbrt.f64 (/.f64 angle 180)) 2)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2) (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 0)) b) (/.f64 1 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b))))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 angle) 2) (/.f64 (cbrt.f64 angle) (/.f64 180 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	26.1b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (expm1.f64 (log1p.f64 (.f64 (PI.f64) (/.f64 angle 180))))) b) (/.f64 1 (.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) b))))
	25.6b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (expm1.f64 (log1p.f64 (.f64 (sin.f64 (/.f64 (*.f64 (PI.f64) angle) 180)) b))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (pow.f64 (cbrt.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))))) 3) 2))
	21.3b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 angle) 2) (/.f64 (cbrt.f64 angle) (/.f64 180 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (.f64 (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) (pow.f64 (cbrt.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	25.5b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 1/180 (.f64 angle (.f64 (PI.f64) b))) (/.f64 1 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b))))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2) (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 0))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.3b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (cbrt.f64 (PI.f64)) (.f64 (/.f64 angle 180) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64)))))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (fma.f64 (cbrt.f64 b) (.f64 (sin.f64 (/.f64 (*.f64 (PI.f64) angle) 180)) (pow.f64 (cbrt.f64 b) 2)) 0) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (cbrt.f64 (PI.f64)) (.f64 (/.f64 angle 180) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64)))))) 2))
	44.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (sqrt.f64 angle) (/.f64 (sqrt.f64 angle) (/.f64 180 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 angle) 2) (/.f64 (cbrt.f64 angle) (/.f64 180 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64))))) b) (/.f64 1 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b))))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 angle 180))) 3))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) angle)) 2) (/.f64 (cbrt.f64 (*.f64 (PI.f64) angle)) 180)))) 2))
	21.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (sqrt.f64 (PI.f64)) (.f64 (/.f64 angle 180) (sqrt.f64 (PI.f64))) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	25.6b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (expm1.f64 (log1p.f64 (/.f64 (*.f64 (PI.f64) angle) 180))))) 2))
	43.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (pow.f64 (.f64 b (sin.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 angle 180))) 2))) 2))
	22.1b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (fma.f64 1/1080 (/.f64 (.f64 angle (PI.f64)) b) (fma.f64 7/2099520000 (/.f64 (.f64 (pow.f64 angle 3) (pow.f64 (PI.f64) 3)) b) (/.f64 180 (.f64 angle (*.f64 (PI.f64) b)))))))
	34.1b	(+.f64 (pow.f64 (.f64 a (cos.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 angle 180)) 3) 1/3))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	22.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (/.f64 1 (.f64 (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 angle 180)) 2) (.f64 (cbrt.f64 (/.f64 angle 180)) (PI.f64)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64))))) b))))
	24.2b	(+.f64 (pow.f64 (.f64 a 1) 2) (.f64 (sin.f64 (/.f64 (.f64 (PI.f64) angle) 180)) (.f64 (.f64 (sin.f64 (/.f64 (.f64 (PI.f64) angle) 180)) b) b)))
	34.5b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (log.f64 (exp.f64 (/.f64 1 (.f64 (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180))) b))))))
	21.2b	(+.f64 (pow.f64 (.f64 a (/.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 3) (+.f64 (pow.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 2) (+.f64 0 (.f64 (cos.f64 (.f64 (PI.f64) (/.f64 angle 180))) 0))))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.2b	(+.f64 (pow.f64 (.f64 a (cos.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (.f64 0 (PI.f64)))))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (PI.f64) (/.f64 angle 180)))) 2))
	21.9b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (/.f64 1 (.f64 (sin.f64 (+.f64 (fma.f64 (cbrt.f64 (PI.f64)) (.f64 (/.f64 angle 180) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64))))) b))))
	22.0b	(+.f64 (pow.f64 (.f64 a 1) 2) (/.f64 (.f64 (sin.f64 (.f64 (PI.f64) (/.f64 angle 180))) b) (/.f64 1 (.f64 (sin.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 angle 180)) (neg.f64 (.f64 0 (PI.f64)))) (fma.f64 0 (PI.f64) (*.f64 0 (PI.f64))))) b))))

Compiler

Compiled 9564 to 6676 computations (30.2% saved)

regimes3.5s (18.1%)

Accuracy

Total 1.7b remaining (8.3%)

Threshold costs 0b (0%)

Counts

377 → 1

Compiler

Compiled 81564 to 65161 computations (20.1% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	18	26
2	17	26

end733.0ms (3.8%)

Compiler: Compiled 1300 to 1023 computations (21.3% saved)

Details

analyze2.1s (10.6%)

sample7.9s (40.4%)

simplify39.0ms (0.2%)

prune2.0ms (0%)

localize12.0ms (0.1%)

series33.0ms (0.2%)

rewrite86.0ms (0.4%)

simplify63.0ms (0.3%)

prune847.0ms (4.4%)

localize10.0ms (0.1%)

series13.0ms (0.1%)

rewrite57.0ms (0.3%)

simplify44.0ms (0.2%)

prune824.0ms (4.2%)

localize11.0ms (0.1%)

series51.0ms (0.3%)

rewrite77.0ms (0.4%)

simplify38.0ms (0.2%)

prune1.9s (9.5%)

localize10.0ms (0.1%)

series43.0ms (0.2%)

rewrite94.0ms (0.5%)

simplify49.0ms (0.3%)

prune1.0s (5.2%)

regimes3.5s (18.1%)

simplify1.0ms (0%)

end733.0ms (3.8%)

Profiling