Details

analyze1.6s (13.1%)

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)

sample3.8s (32.1%)

Alt Table

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

Results

2.4s	3548×	body	1024	valid
588.0ms	1445×	body	512	valid
396.0ms	2479×	body	128	valid
243.0ms	176×	body	2048	valid
174.0ms	608×	body	256	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 62 to 42 computations (32.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
✓	0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
✓	2.6b	(cos.f64 (+.f64 a b))

series77.0ms (0.7%)

Counts

3 → 52

Calls

3 calls:

45.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
27.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
4.0ms	(cos.f64 (+.f64 a b))

rewrite99.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

692×	`prod-diff_binary64`
214×	`fma-def_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
125×	`egg-rr`

Counts

3 → 125

Calls

3 calls:

95.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
95.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
95.0ms	(cos.f64 (+.f64 a b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	200	31
2	2736	31
3	4800	31
4	5016	31
0	0	0
1	0	0

prune223.0ms (1.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	162	15	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	15	178

Error

0.1b

Counts

178 → 15

Alt Table

Status	Error	Program
	22.3b	(.f64 r (/.f64 (sin.f64 b) (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) (sin.f64 a))))))
	15.4b	(.f64 r (/.f64 (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)))) (cos.f64 (-.f64 a b)))))
	0.9b	(.f64 r (/.f64 (sin.f64 b) (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) (sin.f64 a))))))
	0.5b	(.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 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
	15.2b	(/.f64 (*.f64 (sin.f64 b) r) (cos.f64 (+.f64 a b)))
	15.9b	(.f64 r (.f64 (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) 2)))
	32.3b	(.f64 r (+.f64 (/.f64 (sin.f64 b) (cos.f64 b)) (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 b) 2) a) (pow.f64 (cos.f64 b) 2)) (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 b) 3) (pow.f64 a 2)) (pow.f64 (cos.f64 b) 3)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 b) (pow.f64 a 2)) (cos.f64 b))) (+.f64 (.f64 5/6 (/.f64 (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 a 3)) (pow.f64 (cos.f64 b) 2))) (/.f64 (.f64 (pow.f64 (sin.f64 b) 4) (pow.f64 a 3)) (pow.f64 (cos.f64 b) 4))))))))
	31.8b	(.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 (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))))))))
	15.3b	(.f64 r (.f64 (sin.f64 b) (/.f64 1 (cos.f64 (+.f64 a b)))))
	0.5b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 1 (.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)))))))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 1 (.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))))))
	0.5b	(.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)))))))))
	15.9b	(.f64 r (.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 b)) 2) 1) (/.f64 (cbrt.f64 (sin.f64 b)) (cos.f64 (+.f64 a b)))))
	15.3b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))

Compiler

Compiled 5024 to 1617 computations (67.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series197.0ms (1.7%)

Counts

4 → 76

Calls

4 calls:

109.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
63.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
15.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
9.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

rewrite83.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

311×	`fma-neg_binary64`
275×	`expm1-udef_binary64`
275×	`log1p-udef_binary64`
154×	`egg-rr`
153×	`add-sqr-sqrt_binary64`

Counts

4 → 154

Calls

4 calls:

79.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
79.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
79.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
79.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	75
1	292	39
2	3971	39
3	5113	39
0	0	0
1	0	0

prune463.0ms (3.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	225	5	230
Fresh	7	7	14
Picked	1	0	1
Done	0	0	0
Total	233	12	245

Error

0.1b

Counts

245 → 12

Alt Table

Status	Error	Program
	0.5b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 1 (.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)))))))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))
▶	0.4b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.7b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 b)) 2) (.f64 (cbrt.f64 (cos.f64 b)) (cos.f64 a)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
	31.8b	(.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 (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))))))))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 1 (.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))))))
	14.5b	(.f64 r (.f64 (/.f64 (sin.f64 b) (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))) (+.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (*.f64 (sin.f64 b) (sin.f64 a)) (cos.f64 (-.f64 b a))))))
	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)))))))))
	15.9b	(.f64 r (.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 b)) 2) 1) (/.f64 (cbrt.f64 (sin.f64 b)) (cos.f64 (+.f64 a b)))))
	15.3b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
	15.9b	(.f64 r (.f64 (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) 2)))

Compiler

Compiled 5686 to 1652 computations (70.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series213.0ms (1.8%)

Counts

4 → 52

Calls

4 calls:

179.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
15.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
11.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
7.0ms	(*.f64 (sin.f64 b) r)

rewrite88.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

317×	`fma-neg_binary64`
277×	`expm1-udef_binary64`
277×	`log1p-udef_binary64`
155×	`egg-rr`
154×	`add-sqr-sqrt_binary64`

Counts

4 → 155

Calls

4 calls:

83.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
83.0ms	(*.f64 (sin.f64 b) r)
83.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
83.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	58
1	293	34
2	4064	34
3	5221	34
0	0	0
1	0	0

prune325.0ms (2.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	201	6	207
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	206	13	219

Error

0.0b

Counts

219 → 13

Alt Table

Status	Error	Program
	0.4b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))
✓	0.4b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
▶	0.4b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
	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)))))))))
	0.5b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) 3)) (+.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (-.f64 (.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))))))
	15.9b	(.f64 r (.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 b)) 2) 1) (/.f64 (cbrt.f64 (sin.f64 b)) (cos.f64 (+.f64 a b)))))
	0.7b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 a)) 2) (.f64 (cbrt.f64 (cos.f64 a)) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
	15.3b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
	0.7b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 b)) 2) (.f64 (cbrt.f64 (cos.f64 b)) (cos.f64 a)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
	31.8b	(.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 (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))))))))
	15.9b	(.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 b) r)) 2) (.f64 (cbrt.f64 (.f64 (sin.f64 b) r)) (/.f64 1 (cos.f64 (+.f64 b a)))))
	15.9b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 b) r)) 2) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 b a))) 2)) (cbrt.f64 (/.f64 (*.f64 (sin.f64 b) r) (cos.f64 (+.f64 b a)))))
	28.6b	(/.f64 (pow.f64 (sqrt.f64 (.f64 (sin.f64 b) r)) 2) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))

Compiler

Compiled 5325 to 1405 computations (73.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
✓	0.3b	(.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))
✓	0.4b	(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))))
✓	0.4b	(pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 2)

series775.0ms (6.5%)

Counts

4 → 108

Calls

4 calls:

568.0ms	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
162.0ms	(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))))
25.0ms	(.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))
18.0ms	(pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 2)

rewrite88.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

353×	`log1p-udef_binary64`
331×	`prod-diff_binary64`
224×	`add-sqr-sqrt_binary64`
219×	`log1p-expm1-u_binary64`
219×	`expm1-log1p-u_binary64`

Counts

4 → 128

Calls

4 calls:

82.0ms	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
82.0ms	(.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))
82.0ms	(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))))
82.0ms	(pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	128
1	446	42
2	4217	42
3	5282	42
0	0	0
1	0	0

prune373.0ms (3.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	230	6	236
Fresh	5	6	11
Picked	1	0	1
Done	0	1	1
Total	236	13	249

Error

0.0b

Counts

249 → 13

Alt Table

Status	Error	Program
	15.9b	(.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 b) r)) 2) (.f64 (cbrt.f64 (.f64 (sin.f64 b) r)) (/.f64 1 (cos.f64 (+.f64 b a)))))
	0.5b	(/.f64 (.f64 (sin.f64 b) r) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a))) (pow.f64 (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a))) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (pow.f64 (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a))) 2) (.f64 (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a))) (pow.f64 (cbrt.f64 (*.f64 (sin.f64 b) (sin.f64 a))) 2)))))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))
	15.3b	(.f64 (/.f64 (.f64 (sin.f64 b) r) (+.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 2))) (cos.f64 (-.f64 b a)))
✓	0.4b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.5b	(/.f64 (.f64 r (+.f64 (.f64 (sin.f64 a) (pow.f64 (sin.f64 b) 2)) (.f64 (sin.f64 b) (.f64 (cos.f64 a) (cos.f64 b))))) (-.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))))
	0.6b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 6)) (.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
	0.7b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 b)) 2) (.f64 (cbrt.f64 (cos.f64 b)) (cos.f64 a)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
	31.8b	(.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 (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))))))))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) -1))) (fma.f64 (.f64 (sin.f64 b) (sin.f64 a)) -1 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) -1))))
	0.5b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (expm1.f64 (log1p.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2))) (.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
	28.6b	(/.f64 (pow.f64 (sqrt.f64 (.f64 (sin.f64 b) r)) 2) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.7b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 a)) 2) (.f64 (cbrt.f64 (cos.f64 a)) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))

Compiler

Compiled 8953 to 2754 computations (69.2% saved)

regimes3.2s (26.9%)

Accuracy

Total 0.3b remaining (82.2%)

Threshold costs 0.3b (82.2%)

Counts

383 → 1

Compiler

Compiled 44547 to 26612 computations (40.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	21	26
2	31	26
3	37	26
4	41	26
5	42	26
6	42	26

end236.0ms (2%)

Compiler: Compiled 491 to 260 computations (47% saved)

Details

analyze1.6s (13.1%)

sample3.8s (32.1%)

localize7.0ms (0.1%)

series77.0ms (0.7%)

rewrite99.0ms (0.8%)

prune223.0ms (1.9%)

localize12.0ms (0.1%)

series197.0ms (1.7%)

rewrite83.0ms (0.7%)

prune463.0ms (3.9%)

localize12.0ms (0.1%)

series213.0ms (1.8%)

rewrite88.0ms (0.7%)

prune325.0ms (2.7%)

localize17.0ms (0.1%)

series775.0ms (6.5%)

rewrite88.0ms (0.7%)

prune373.0ms (3.1%)

regimes3.2s (26.9%)

simplify5.0ms (0%)

end236.0ms (2%)

Profiling