Details

analyze1.4s (13%)

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
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample4.0s (36.5%)

Results

2.4s	3599×	body	1024	valid
693.0ms	1425×	body	512	valid
384.0ms	2444×	body	128	valid
296.0ms	230×	body	2048	valid
163.0ms	558×	body	256	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
2	17	14
3	20	14
4	21	14

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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

15.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	15.3b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))))
▶	15.3b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))

Compiler

Compiled 69 to 44 computations (36.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 r (sin.f64 b))
✓	0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
✓	3.0b	(cos.f64 (+.f64 a b))

series54.0ms (0.5%)

Counts

3 → 68

Calls

3 calls:

43.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
6.0ms	(*.f64 r (sin.f64 b))
5.0ms	(cos.f64 (+.f64 a b))

rewrite61.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

597×	`prod-diff_binary64`
211×	`fma-def_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
125×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	200	26
2	2926	26

Stop Event

1×	node limit

Counts

3 → 124

Calls

3 calls:

58.0ms	(*.f64 r (sin.f64 b))
58.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
58.0ms	(cos.f64 (+.f64 a b))

simplify36.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
662×	`associate-/l*_binary64`
530×	`fma-def_binary64`
309×	`associate-/r*_binary64`
152×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1221
1	414	1211
2	1444	1163

Stop Event

1×	node limit

Counts

192 → 164

prune269.0ms (2.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	151	13	164
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	153	13	166

Error

0.1b

Counts

166 → 13

Alt Table

Status	Error	Program
	15.3b	(.f64 (sin.f64 b) (.f64 r (/.f64 1 (cos.f64 (+.f64 a b)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)) (fma.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b)) (fma.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))))))
▶	0.3b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))))
	15.3b	(*.f64 (/.f64 r (cos.f64 (+.f64 a b))) (sin.f64 b))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a)))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a))) (.f64 (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a))) (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a))))))) (fma.f64 (neg.f64 (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (.f64 (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a))) (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (.f64 (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a))) (.f64 (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a))) (cbrt.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))
	30.4b	(fma.f64 (/.f64 (sin.f64 a) (pow.f64 (cos.f64 a) 2)) (.f64 b (.f64 b r)) (*.f64 (/.f64 r (cos.f64 a)) b))
	30.5b	(+.f64 (/.f64 (.f64 b r) (cos.f64 a)) (/.f64 (.f64 (sin.f64 a) (*.f64 (pow.f64 b 2) r)) (pow.f64 (cos.f64 a) 2)))
	29.8b	(*.f64 (/.f64 r (sqrt.f64 (cos.f64 (+.f64 a b)))) (/.f64 (sin.f64 b) (sqrt.f64 (cos.f64 (+.f64 a b)))))
	15.4b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	21.8b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (sqrt.f64 (.f64 (cos.f64 a) (cos.f64 b))) (sqrt.f64 (.f64 (cos.f64 a) (cos.f64 b))) (neg.f64 (.f64 (cbrt.f64 (sin.f64 b)) (.f64 (sin.f64 a) (cbrt.f64 (pow.f64 (sin.f64 b) 2)))))) (fma.f64 (neg.f64 (cbrt.f64 (sin.f64 b))) (.f64 (sin.f64 a) (cbrt.f64 (pow.f64 (sin.f64 b) 2))) (.f64 (cbrt.f64 (sin.f64 b)) (.f64 (sin.f64 a) (cbrt.f64 (pow.f64 (sin.f64 b) 2)))))))
	0.8b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 a) (cos.f64 b))) (cbrt.f64 (.f64 (cos.f64 a) (cos.f64 b)))) (cbrt.f64 (.f64 (cos.f64 a) (cos.f64 b))) (neg.f64 (.f64 (cbrt.f64 (sin.f64 b)) (.f64 (sin.f64 a) (cbrt.f64 (pow.f64 (sin.f64 b) 2)))))) (fma.f64 (neg.f64 (cbrt.f64 (sin.f64 b))) (.f64 (sin.f64 a) (cbrt.f64 (pow.f64 (sin.f64 b) 2))) (.f64 (cbrt.f64 (sin.f64 b)) (.f64 (sin.f64 a) (cbrt.f64 (pow.f64 (sin.f64 b) 2)))))))
	30.6b	(fma.f64 1/2 (.f64 (/.f64 (.f64 (sin.f64 b) (.f64 a a)) (cos.f64 b)) r) (fma.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r (fma.f64 5/6 (.f64 (/.f64 (pow.f64 a 3) (/.f64 (pow.f64 (cos.f64 b) 2) r)) (pow.f64 (sin.f64 b) 2)) (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 4) (pow.f64 (cos.f64 b) 4)) (.f64 (pow.f64 a 3) r) (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 3) (pow.f64 (cos.f64 b) 3)) (.f64 a (.f64 a r)) (.f64 (/.f64 (*.f64 a r) (pow.f64 (cos.f64 b) 2)) (pow.f64 (sin.f64 b) 2)))))))

Compiler

Compiled 4934 to 1564 computations (68.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))
	0.1b	(*.f64 r (sin.f64 b))
✓	0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
✓	0.2b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))))

series129.0ms (1.2%)

Counts

3 → 76

Calls

3 calls:

103.0ms

(/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))

16.0ms

(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))

9.0ms

(*.f64 (sin.f64 b) (sin.f64 a))

rewrite147.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

779×	`prod-diff_binary64`
427×	`egg-rr`
146×	`add-sqr-sqrt_binary64`
134×	`log1p-expm1-u_binary64`
134×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	276	28
2	3867	28

Stop Event

1×	node limit

Counts

3 → 427

Calls

3 calls:

129.0ms

(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))

129.0ms

(*.f64 (sin.f64 b) (sin.f64 a))

129.0ms

(/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
667×	`associate-/l*_binary64`
601×	`fma-def_binary64`
236×	`cancel-sign-sub-inv_binary64`
116×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	1911
1	464	1901
2	1587	1839

Stop Event

1×	node limit

Counts

503 → 478

prune933.0ms (8.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	493	9	502
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	501	14	515

Error

0.0b

Counts

515 → 14

Alt Table

Status	Error	Program
	15.3b	(.f64 (sin.f64 b) (.f64 r (/.f64 1 (cos.f64 (+.f64 a b)))))
	0.7b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 a)) 2) (.f64 (cbrt.f64 (cos.f64 a)) (cos.f64 b)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b))) (pow.f64 (cbrt.f64 (sin.f64 a)) 2) (.f64 (*.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 b) (sin.f64 a)))) 1))))
	1.2b	(/.f64 (pow.f64 (cbrt.f64 (.f64 r (sin.f64 b))) 3) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))))
	30.4b	(fma.f64 (/.f64 (sin.f64 a) (pow.f64 (cos.f64 a) 2)) (.f64 b (.f64 b r)) (*.f64 (/.f64 r (cos.f64 a)) b))
	30.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 a)) (sin.f64 b)) (sqrt.f64 (sin.f64 a))))) (fma.f64 (neg.f64 (.f64 (sqrt.f64 (sin.f64 a)) (sin.f64 b))) (sqrt.f64 (sin.f64 a)) (.f64 (*.f64 (sqrt.f64 (sin.f64 a)) (sin.f64 b)) (sqrt.f64 (sin.f64 a))))))
	26.6b	(fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) (.f64 r a) (.f64 (/.f64 r (cos.f64 b)) (sin.f64 b)))
▶	0.4b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a))))))))
	29.8b	(*.f64 (/.f64 r (sqrt.f64 (cos.f64 (+.f64 a b)))) (/.f64 (sin.f64 b) (sqrt.f64 (cos.f64 (+.f64 a b)))))
	15.4b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	0.7b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 a)) 2) (.f64 (cbrt.f64 (cos.f64 a)) (cos.f64 b)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a))) (pow.f64 (cbrt.f64 (sin.f64 b)) 2) (.f64 (*.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a))) (pow.f64 (cbrt.f64 (sin.f64 b)) 2) (.f64 (*.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)))))
	0.7b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (.f64 (cos.f64 a) (pow.f64 (cbrt.f64 (cos.f64 b)) 2)) (cbrt.f64 (cos.f64 b)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b))) (pow.f64 (cbrt.f64 (sin.f64 a)) 2) (.f64 (*.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2)))))

Compiler

Compiled 19811 to 4308 computations (78.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a)))))
✓	0.3b	(.f64 (.f64 (sin.f64 b) (sin.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))
✓	0.3b	(/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (cos.f64 a) (cos.f64 b) (*.f64 (sin.f64 b) (sin.f64 a))))
✓	0.3b	(.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (cos.f64 a) (cos.f64 b)))

series483.0ms (4.4%)

Counts

4 → 108

Calls

4 calls:

346.0ms	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a)))))
97.0ms	(/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (cos.f64 a) (cos.f64 b) (*.f64 (sin.f64 b) (sin.f64 a))))
20.0ms	(.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (cos.f64 a) (cos.f64 b)))
19.0ms	(.f64 (.f64 (sin.f64 b) (sin.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))

rewrite45.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

201×	`add-sqr-sqrt_binary64`
193×	`log1p-expm1-u_binary64`
193×	`expm1-log1p-u_binary64`
188×	`add-cbrt-cube_binary64`
187×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	114
1	394	74

Stop Event

1×	node limit

Counts

4 → 98

Calls

4 calls:

42.0ms	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a)))))
42.0ms	(.f64 (.f64 (sin.f64 b) (sin.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))
42.0ms	(/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (cos.f64 a) (cos.f64 b) (*.f64 (sin.f64 b) (sin.f64 a))))
42.0ms	(.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (cos.f64 a) (cos.f64 b)))

simplify74.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

889×	`times-frac_binary64`
389×	`cancel-sign-sub-inv_binary64`
203×	`fma-neg_binary64`
196×	`associate-r_binary64`
177×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	4013
1	614	3893
2	2217	3804

Stop Event

1×	node limit

Counts

206 → 171

prune358.0ms (3.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	166	5	171
Fresh	5	8	13
Picked	0	1	1
Done	0	0	0
Total	171	14	185

Error

0.0b

Counts

185 → 14

Alt Table

Status	Error	Program
	15.3b	(.f64 (sin.f64 b) (.f64 r (/.f64 1 (cos.f64 (+.f64 a b)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 b) (sin.f64 a)))) 1))))
	0.7b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 a)) 2) (.f64 (cbrt.f64 (cos.f64 a)) (cos.f64 b)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a))) (pow.f64 (cbrt.f64 (sin.f64 b)) 2) (.f64 (*.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)))))
	0.4b	(/.f64 (.f64 (sin.f64 b) (.f64 r (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))) (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2))))
	0.7b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (.f64 (cos.f64 a) (pow.f64 (cbrt.f64 (cos.f64 b)) 2)) (cbrt.f64 (cos.f64 b)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b))) (pow.f64 (cbrt.f64 (sin.f64 a)) 2) (.f64 (*.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2)))))
	15.3b	(.f64 (/.f64 (sin.f64 b) 1) (/.f64 r (/.f64 (.f64 (cos.f64 (-.f64 b a)) (cos.f64 (+.f64 b a))) (cos.f64 (-.f64 b a)))))
✓	0.4b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a))))))))
	0.6b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (pow.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a))) 2) 3)) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a)))))
	0.6b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 6)) (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a)))))
	26.6b	(fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) (.f64 r a) (.f64 (/.f64 r (cos.f64 b)) (sin.f64 b)))
▶	0.4b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2))) (fma.f64 (cos.f64 b) (cos.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))
	15.4b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a))) (pow.f64 (cbrt.f64 (sin.f64 b)) 2) (.f64 (*.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)))))

Compiler

Compiled 6740 to 2063 computations (69.4% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2))) (fma.f64 (cos.f64 b) (cos.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))
✓	0.2b	(pow.f64 (sin.f64 b) 2)
✓	0.3b	(pow.f64 (sin.f64 a) 2)
✓	0.3b	(/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2))) (fma.f64 (cos.f64 b) (cos.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))

series454.0ms (4.2%)

Counts

4 → 68

Calls

4 calls:

346.0ms	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2))) (fma.f64 (cos.f64 b) (cos.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))
96.0ms	(/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2))) (fma.f64 (cos.f64 b) (cos.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))
9.0ms	(pow.f64 (sin.f64 a) 2)
3.0ms	(pow.f64 (sin.f64 b) 2)

rewrite39.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

228×	`add-sqr-sqrt_binary64`
222×	`log1p-expm1-u_binary64`
222×	`expm1-log1p-u_binary64`
216×	`add-cbrt-cube_binary64`
214×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	104
1	470	84

Stop Event

1×	node limit

Counts

4 → 70

Calls

4 calls:

37.0ms	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2))) (fma.f64 (cos.f64 b) (cos.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))
37.0ms	(pow.f64 (sin.f64 b) 2)
37.0ms	(pow.f64 (sin.f64 a) 2)
37.0ms	(/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2))) (fma.f64 (cos.f64 b) (cos.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))

simplify59.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

889×	`times-frac_binary64`
719×	`associate-/l*_binary64`
635×	`fma-def_binary64`
165×	`cancel-sign-sub-inv_binary64`
130×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	3179
1	509	3081
2	1723	3039

Stop Event

1×	node limit

Counts

138 → 123

prune264.0ms (2.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	124	13	137

Error

0.0b

Counts

137 → 13

Alt Table

Status	Error	Program
	15.3b	(.f64 (sin.f64 b) (.f64 r (/.f64 1 (cos.f64 (+.f64 a b)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 b) (sin.f64 a)))) 1))))
	0.7b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 a)) 2) (.f64 (cbrt.f64 (cos.f64 a)) (cos.f64 b)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a))) (pow.f64 (cbrt.f64 (sin.f64 b)) 2) (.f64 (*.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)))))
	0.4b	(/.f64 (.f64 (sin.f64 b) (.f64 r (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))) (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2))))
	0.7b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (.f64 (cos.f64 a) (pow.f64 (cbrt.f64 (cos.f64 b)) 2)) (cbrt.f64 (cos.f64 b)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b))) (pow.f64 (cbrt.f64 (sin.f64 a)) 2) (.f64 (*.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2)))))
	15.3b	(.f64 (/.f64 (sin.f64 b) 1) (/.f64 r (/.f64 (.f64 (cos.f64 (-.f64 b a)) (cos.f64 (+.f64 b a))) (cos.f64 (-.f64 b a)))))
✓	0.4b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a))))))))
	0.6b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 6)) (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a)))))
	0.4b	(.f64 (/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2)))) (fma.f64 (cos.f64 a) (cos.f64 b) (*.f64 (sin.f64 a) (sin.f64 b))))
	15.4b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (log.f64 (exp.f64 (pow.f64 (sin.f64 a) 2))))) (fma.f64 (cos.f64 b) (cos.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a))) (pow.f64 (cbrt.f64 (sin.f64 b)) 2) (.f64 (*.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)))))

Compiler

Compiled 4647 to 1963 computations (57.8% saved)

regimes1.7s (15.5%)

Accuracy

Total 0.3b remaining (81.2%)

Threshold costs 0.3b (81.2%)

Counts

321 → 1

Compiler

Compiled 39288 to 20950 computations (46.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	30
1	21	30
2	23	30
3	24	30

Stop Event

1×

saturated

end259.0ms (2.4%)

Compiler: Compiled 510 to 282 computations (44.7% saved)

Details

analyze1.4s (13%)

sample4.0s (36.5%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series54.0ms (0.5%)

rewrite61.0ms (0.6%)

simplify36.0ms (0.3%)

prune269.0ms (2.5%)

localize14.0ms (0.1%)

series129.0ms (1.2%)

rewrite147.0ms (1.3%)

simplify79.0ms (0.7%)

prune933.0ms (8.6%)

localize18.0ms (0.2%)

series483.0ms (4.4%)

rewrite45.0ms (0.4%)

simplify74.0ms (0.7%)

prune358.0ms (3.3%)

localize22.0ms (0.2%)

series454.0ms (4.2%)

rewrite39.0ms (0.4%)

simplify59.0ms (0.5%)

prune264.0ms (2.4%)

regimes1.7s (15.5%)

simplify2.0ms (0%)

end259.0ms (2.4%)

Profiling