Details

analyze1.5s (13.8%)

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)

sample3.9s (35.5%)

Results

2.4s	3600×	body	1024	valid
604.0ms	1458×	body	512	valid
394.0ms	2388×	body	128	valid
284.0ms	207×	body	2048	valid
187.0ms	603×	body	256	valid
1.0ms	1×	body	1024	invalid

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
2	17	14
3	21	14
4	22	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

16.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	17.0b	(/.f64 r (/.f64 (cos.f64 (+.f64 b a)) (sin.f64 b)))
▶	16.9b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))

Compiler

Compiled 69 to 44 computations (36.2% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 b)
✓	0.1b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
✓	0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
✓	4.2b	(cos.f64 (+.f64 a b))

series68.0ms (0.6%)

Counts

4 → 56

Calls

4 calls:

39.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
24.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
4.0ms	(cos.f64 (+.f64 a b))
1.0ms	(sin.f64 b)

rewrite62.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

588×	`prod-diff_binary64`
214×	`fma-def_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
141×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	34
1	200	34
2	2864	34

Stop Event

1×	node limit

Counts

4 → 141

Calls

4 calls:

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

simplify41.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

753×	`fma-def_binary64`
639×	`associate-l_binary64`
438×	`associate-/r*_binary64`
196×	`associate-/r/_binary64`
178×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	1474
1	513	1472
2	1839	1406

Stop Event

1×	node limit

Counts

197 → 192

prune275.0ms (2.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	177	15	192
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	178	16	194

Error

0.1b

Counts

194 → 16

Alt Table

Status	Error	Program
	24.0b	(.f64 r (/.f64 (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 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))))))
	31.9b	(+.f64 (/.f64 (.f64 b r) (cos.f64 a)) (+.f64 (/.f64 (.f64 (sin.f64 a) (.f64 r (pow.f64 b 2))) (pow.f64 (cos.f64 a) 2)) (+.f64 (.f64 2/3 (/.f64 (.f64 (sin.f64 a) (.f64 (pow.f64 b 4) r)) (pow.f64 (cos.f64 a) 2))) (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 a) 3) (.f64 (pow.f64 b 4) r)) (pow.f64 (cos.f64 a) 4)) (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 a) 2) (.f64 (pow.f64 b 3) r)) (pow.f64 (cos.f64 a) 3)) (.f64 1/3 (/.f64 (.f64 (pow.f64 b 3) r) (cos.f64 a))))))))
▶	0.3b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))))))
	17.0b	(/.f64 (*.f64 (sin.f64 b) r) (cos.f64 (+.f64 a b)))
	39.3b	(*.f64 r (pow.f64 (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) 2))
	0.9b	(.f64 r (/.f64 (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 (.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)))))))))
	39.8b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) r) 3))
	0.5b	(.f64 r (/.f64 (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)))))))))
	38.3b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) r)) 2)
	32.4b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sqrt.f64 (sin.f64 b)) (.f64 (sin.f64 a) (sqrt.f64 (sin.f64 b)))))) (fma.f64 (neg.f64 (sqrt.f64 (sin.f64 b))) (.f64 (sin.f64 a) (sqrt.f64 (sin.f64 b))) (.f64 (sqrt.f64 (sin.f64 b)) (.f64 (sin.f64 a) (sqrt.f64 (sin.f64 b))))))))
	0.5b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (cbrt.f64 (sin.f64 b)) (.f64 (sin.f64 a) (pow.f64 (cbrt.f64 (sin.f64 b)) 2))))) (fma.f64 (neg.f64 (cbrt.f64 (sin.f64 b))) (.f64 (sin.f64 a) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)) (.f64 (cbrt.f64 (sin.f64 b)) (.f64 (sin.f64 a) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)))))))
	0.8b	(.f64 r (/.f64 (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 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))))))
	0.4b	(.f64 r (/.f64 (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))))))))
	17.0b	(/.f64 r (/.f64 (cos.f64 (+.f64 b a)) (sin.f64 b)))
	31.6b	(fma.f64 1/2 (/.f64 (sin.f64 b) (/.f64 (cos.f64 b) (.f64 (.f64 a a) r))) (fma.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 3) (pow.f64 (cos.f64 b) 3)) (.f64 (.f64 a a) r) (.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) (.f64 a r)))))
	0.3b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))

Compiler

Compiled 5937 to 2109 computations (64.5% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))))))
✓	0.2b	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))
✓	0.2b	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))))
✓	51.9b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series229.0ms (2.1%)

Counts

4 → 108

Calls

4 calls:

125.0ms	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))))))
71.0ms	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))))
22.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))
10.0ms	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))

rewrite69.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

288×	`log1p-udef_binary64`
179×	`add-sqr-sqrt_binary64`
165×	`add-cbrt-cube_binary64`
165×	`log1p-expm1-u_binary64`
165×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	115
1	375	90
2	4798	90

Stop Event

1×	node limit

Counts

4 → 107

Calls

4 calls:

66.0ms	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))))))
66.0ms	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))
66.0ms	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))))
66.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

simplify50.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-def_binary64`
673×	`associate-l_binary64`
437×	`associate-/r*_binary64`
196×	`associate-/r/_binary64`
178×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	2338
1	532	2328
2	1877	2244

Stop Event

1×	node limit

Counts

215 → 161

prune355.0ms (3.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	197	3	200
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	203	13	216

Error

0.0b

Counts

216 → 13

Alt Table

Status	Error	Program
	0.9b	(.f64 r (/.f64 (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 (.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)))))))))
	39.8b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) r) 3))
	0.5b	(.f64 r (/.f64 (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)))))))))
	38.3b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) r)) 2)
	32.4b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sqrt.f64 (sin.f64 b)) (.f64 (sin.f64 a) (sqrt.f64 (sin.f64 b)))))) (fma.f64 (neg.f64 (sqrt.f64 (sin.f64 b))) (.f64 (sin.f64 a) (sqrt.f64 (sin.f64 b))) (.f64 (sqrt.f64 (sin.f64 b)) (.f64 (sin.f64 a) (sqrt.f64 (sin.f64 b))))))))
	0.8b	(.f64 r (/.f64 (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 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))))))
	39.3b	(*.f64 r (pow.f64 (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) 2))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a))))))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1))))))
	0.4b	(.f64 r (/.f64 (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))))))))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a)))))))
▶	0.3b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	17.0b	(/.f64 r (/.f64 (cos.f64 (+.f64 b a)) (sin.f64 b)))
	31.6b	(fma.f64 1/2 (/.f64 (sin.f64 b) (/.f64 (cos.f64 b) (.f64 (.f64 a a) r))) (fma.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 3) (pow.f64 (cos.f64 b) 3)) (.f64 (.f64 a a) r) (.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) (.f64 a r)))))

Compiler

Compiled 8015 to 3200 computations (60.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series127.0ms (1.1%)

Counts

4 → 52

Calls

4 calls:

98.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
13.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
9.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
6.0ms	(*.f64 (sin.f64 b) r)

rewrite67.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

277×	`expm1-udef_binary64`
277×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
148×	`log1p-expm1-u_binary64`
148×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	58
1	297	34
2	4363	34

Stop Event

1×	node limit

Counts

4 → 130

Calls

4 calls:

64.0ms	(*.f64 (sin.f64 b) r)
64.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
64.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
64.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))

simplify46.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
673×	`fma-def_binary64`
666×	`associate-/l*_binary64`
311×	`cancel-sign-sub-inv_binary64`
154×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	152	1361
1	495	1343
2	1742	1265

Stop Event

1×	node limit

Counts

182 → 189

prune282.0ms (2.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	180	9	189
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	188	14	202

Error

0.0b

Counts

202 → 14

Alt Table

Status	Error	Program
	28.4b	(fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) (.f64 r a) (.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r))
	32.9b	(/.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) r) 3)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.9b	(.f64 r (/.f64 (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 (.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)))))))))
	0.4b	(/.f64 r (/.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))) (sin.f64 b)))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (pow.f64 (exp.f64 (sin.f64 a)) (sin.f64 b)))))
	1.3b	(/.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 b) r)) 3) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
▶	0.3b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a)))))))
	32.4b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sqrt.f64 (sin.f64 b)) (.f64 (sin.f64 a) (sqrt.f64 (sin.f64 b)))))) (fma.f64 (neg.f64 (sqrt.f64 (sin.f64 b))) (.f64 (sin.f64 a) (sqrt.f64 (sin.f64 b))) (.f64 (sqrt.f64 (sin.f64 b)) (.f64 (sin.f64 a) (sqrt.f64 (sin.f64 b))))))))
	17.1b	(pow.f64 (/.f64 (cos.f64 (+.f64 b a)) (*.f64 (sin.f64 b) r)) -1)
	0.8b	(.f64 r (/.f64 (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 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))))))
	0.4b	(.f64 r (/.f64 (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))))))))
	0.6b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2)) (cbrt.f64 (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (sin.f64 b) (neg.f64 (sin.f64 a)))))
	16.9b	(*.f64 (/.f64 (sin.f64 b) 1) (/.f64 r (cos.f64 (+.f64 b a))))

Compiler

Compiled 5067 to 1653 computations (67.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series128.0ms (1.2%)

Counts

3 → 84

Calls

3 calls:

102.0ms

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

15.0ms

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

11.0ms

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

rewrite84.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

308×	`prod-diff_binary64`
231×	`expm1-udef_binary64`
231×	`log1p-udef_binary64`
202×	`egg-rr`
139×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	54
1	267	48
2	3603	48

Stop Event

1×	node limit

Counts

3 → 202

Calls

3 calls:

76.0ms

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

76.0ms

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

76.0ms

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

simplify46.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
667×	`associate-/l*_binary64`
644×	`fma-def_binary64`
174×	`cancel-sign-sub-inv_binary64`
148×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	2011
1	475	2009
2	1575	1943

Stop Event

1×	node limit

Counts

286 → 256

prune535.0ms (4.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	277	2	279
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	282	11	293

Error

0.0b

Counts

293 → 11

Alt Table

Status	Error	Program
	17.1b	(pow.f64 (/.f64 (cos.f64 (+.f64 b a)) (*.f64 (sin.f64 b) r)) -1)
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (neg.f64 (sin.f64 a))))) (fma.f64 (sin.f64 b) (neg.f64 (sin.f64 a)) (*.f64 (sin.f64 b) (neg.f64 (sin.f64 a))))))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (pow.f64 (exp.f64 (sin.f64 a)) (sin.f64 b)))))
	1.3b	(/.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 b) r)) 3) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.8b	(.f64 r (/.f64 (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 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))))))
	32.9b	(/.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) r) 3)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.4b	(/.f64 r (/.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))) (sin.f64 b)))
	0.7b	(/.f64 (.f64 (sin.f64 b) r) (+.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 r (/.f64 (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))))))))
	0.6b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2)) (cbrt.f64 (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (sin.f64 b) (neg.f64 (sin.f64 a)))))
	16.9b	(*.f64 (/.f64 (sin.f64 b) 1) (/.f64 r (cos.f64 (+.f64 b a))))

Compiler

Compiled 9555 to 2339 computations (75.5% saved)

regimes2.9s (25.9%)

Accuracy

Total 0.3b remaining (80.6%)

Threshold costs 0.3b (80.6%)

Counts

391 → 1

Compiler

Compiled 53901 to 30908 computations (42.7% 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	13	26
1	19	26
2	21	26
3	22	26

Stop Event

1×

saturated

end229.0ms (2.1%)

Compiler: Compiled 380 to 205 computations (46.1% saved)

Details

analyze1.5s (13.8%)

sample3.9s (35.5%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series68.0ms (0.6%)

rewrite62.0ms (0.6%)

simplify41.0ms (0.4%)

prune275.0ms (2.5%)

localize18.0ms (0.2%)

series229.0ms (2.1%)

rewrite69.0ms (0.6%)

simplify50.0ms (0.5%)

prune355.0ms (3.2%)

localize12.0ms (0.1%)

series127.0ms (1.1%)

rewrite67.0ms (0.6%)

simplify46.0ms (0.4%)

prune282.0ms (2.5%)

localize13.0ms (0.1%)

series128.0ms (1.2%)

rewrite84.0ms (0.8%)

simplify46.0ms (0.4%)

prune535.0ms (4.8%)

regimes2.9s (25.9%)

simplify2.0ms (0%)

end229.0ms (2.1%)

Profiling