Details

analyze1.5s (13.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
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)

sample4.2s (37.7%)

Alt Table

Status	Error	Program
▶	15.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))

Results

2.5s	3548×	body	1024	valid
783.0ms	1445×	body	512	valid
398.0ms	2479×	body	128	valid
245.0ms	176×	body	2048	valid
187.0ms	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
✓	0.1b	(*.f64 r (sin.f64 b))
✓	0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
✓	2.6b	(cos.f64 (+.f64 a b))

series56.0ms (0.5%)

Counts

3 → 68

Calls

3 calls:

44.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
7.0ms	(*.f64 r (sin.f64 b))
4.0ms	(cos.f64 (+.f64 a b))

rewrite100.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

701×	`prod-diff_binary64`
211×	`fma-def_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
126×	`egg-rr`

Counts

3 → 126

Calls

3 calls:

96.0ms	(*.f64 r (sin.f64 b))
96.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
96.0ms	(cos.f64 (+.f64 a b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	200	26
2	2799	26
3	4792	26
4	5009	26
0	0	0
1	0	0

prune317.0ms (2.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	178	16	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	179	16	195

Error

0.1b

Counts

195 → 16

Alt Table

Status	Error	Program
	15.3b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	22.3b	(/.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 (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)))))
	28.0b	(+.f64 (/.f64 (.f64 (sin.f64 b) r) (cos.f64 b)) (/.f64 (.f64 (pow.f64 (sin.f64 b) 2) (*.f64 a r)) (pow.f64 (cos.f64 b) 2)))
	31.8b	(/.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 (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	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	36.5b	(.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (/.f64 1 (cos.f64 (+.f64 a b)))))
	0.9b	(/.f64 (.f64 r (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 (.f64 r (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))))))
	15.3b	(*.f64 (/.f64 r (cos.f64 (+.f64 a b))) (sin.f64 b))
▶	0.4b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.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 (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 (.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)))))))
	15.9b	(.f64 (pow.f64 (cbrt.f64 (.f64 r (sin.f64 b))) 2) (.f64 (cbrt.f64 (.f64 r (sin.f64 b))) (/.f64 1 (cos.f64 (+.f64 a b)))))
	15.9b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 r (sin.f64 b))) 2) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (cbrt.f64 (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))))
	0.4b	(/.f64 (.f64 r (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)))))
	0.5b	(/.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))))))))

Compiler

Compiled 5039 to 1430 computations (71.6% saved)

localize13.0ms (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 r (sin.f64 b))
✓	0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
✓	0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))

series136.0ms (1.2%)

Counts

4 → 88

Calls

4 calls:

105.0ms	(/.f64 (.f64 r (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))
7.0ms	(*.f64 r (sin.f64 b))

rewrite85.0ms (0.8%)

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:

81.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
81.0ms	(*.f64 r (sin.f64 b))
81.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
81.0ms	(/.f64 (.f64 r (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	58
1	293	34
2	4064	34
3	5221	34
0	0	0
1	0	0

prune508.0ms (4.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	232	11	243
Fresh	9	6	15
Picked	1	0	1
Done	0	0	0
Total	242	17	259

Error

0.0b

Counts

259 → 17

Alt Table

Status	Error	Program
	15.4b	(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (exp.f64 (cos.f64 (+.f64 b a)))))
	15.3b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))))
	0.7b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (.f64 (cos.f64 b) (pow.f64 (cbrt.f64 (cos.f64 a)) 2)) (cbrt.f64 (cos.f64 a)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
	0.4b	(/.f64 (.f64 r (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))))))
	28.6b	(/.f64 (pow.f64 (sqrt.f64 (.f64 r (sin.f64 b))) 2) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	15.3b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	0.5b	(/.f64 (.f64 r (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))))))
	15.9b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 r (sin.f64 b))) 2) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (cbrt.f64 (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))))
	0.7b	(/.f64 (.f64 r (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)))))
▶	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (*.f64 (cos.f64 a) (cos.f64 b))))
	31.8b	(/.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 (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)))))))
	14.5b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (sqrt.f64 (cos.f64 b)) (.f64 (sqrt.f64 (cos.f64 b)) (cos.f64 a)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
	1.2b	(/.f64 (pow.f64 (cbrt.f64 (.f64 r (sin.f64 b))) 3) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (/.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))))))))
	0.7b	(/.f64 (.f64 r (sin.f64 b)) (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)))))
	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))))))))

Compiler

Compiled 6146 to 1558 computations (74.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series140.0ms (1.3%)

Counts

4 → 100

Calls

4 calls:

108.0ms	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (*.f64 (cos.f64 a) (cos.f64 b))))
15.0ms	(+.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (.f64 (cos.f64 a) (cos.f64 b)))
10.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
7.0ms	(*.f64 r (sin.f64 b))

rewrite84.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

318×	`fma-neg_binary64`
275×	`expm1-udef_binary64`
275×	`log1p-udef_binary64`
165×	`add-sqr-sqrt_binary64`
156×	`log1p-expm1-u_binary64`

Counts

4 → 143

Calls

4 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	62
1	312	34
2	4076	34
3	5166	34
0	0	0
1	0	0

prune422.0ms (3.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	243	17	260

Error

0.0b

Counts

260 → 17

Alt Table

Status	Error	Program
	15.4b	(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (exp.f64 (cos.f64 (+.f64 b a)))))
	15.3b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))))
	0.7b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (.f64 (cos.f64 b) (pow.f64 (cbrt.f64 (cos.f64 a)) 2)) (cbrt.f64 (cos.f64 a)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
▶	0.4b	(/.f64 (.f64 r (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))))))
	28.6b	(/.f64 (pow.f64 (sqrt.f64 (.f64 r (sin.f64 b))) 2) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	15.3b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	0.5b	(/.f64 (.f64 r (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))))))
	15.9b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 r (sin.f64 b))) 2) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (cbrt.f64 (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))))
	0.7b	(/.f64 (.f64 r (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)))))
✓	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (*.f64 (cos.f64 a) (cos.f64 b))))
	31.8b	(/.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 (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)))))))
	14.5b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (sqrt.f64 (cos.f64 b)) (.f64 (sqrt.f64 (cos.f64 b)) (cos.f64 a)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
	1.2b	(/.f64 (pow.f64 (cbrt.f64 (.f64 r (sin.f64 b))) 3) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (/.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))))))))
	0.7b	(/.f64 (.f64 r (sin.f64 b)) (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)))))
	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))))))))

Compiler

Compiled 5741 to 1556 computations (72.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 r (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))))))
✓	0.3b	(.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)

series1.3s (11.4%)

Counts

4 → 108

Calls

4 calls:

1.1s	(/.f64 (.f64 r (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))))))
112.0ms	(/.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)))))
27.0ms	(.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))
19.0ms	(pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 2)

rewrite91.0ms (0.8%)

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:

87.0ms	(/.f64 (.f64 r (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))))))
87.0ms	(.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))
87.0ms	(/.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)))))
87.0ms	(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

prune396.0ms (3.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	231	5	236
Fresh	7	8	15
Picked	0	1	1
Done	0	1	1
Total	238	15	253

Error

0.0b

Counts

253 → 15

Alt Table

Status	Error	Program
	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))))
	0.7b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (.f64 (cos.f64 b) (pow.f64 (cbrt.f64 (cos.f64 a)) 2)) (cbrt.f64 (cos.f64 a)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
✓	0.4b	(/.f64 (.f64 r (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))))))
	28.6b	(/.f64 (pow.f64 (sqrt.f64 (.f64 r (sin.f64 b))) 2) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	15.3b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (/.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))))))))
	1.1b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (log.f64 (+.f64 1 (expm1.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))))))
	15.3b	(/.f64 (.f64 r (sin.f64 b)) (.f64 (+.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 2)) (/.f64 1 (cos.f64 (-.f64 b a)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.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))) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
	15.3b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
✓	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (*.f64 (cos.f64 a) (cos.f64 b))))
	31.8b	(/.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 (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)))))))
	14.5b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (sqrt.f64 (cos.f64 b)) (.f64 (sqrt.f64 (cos.f64 b)) (cos.f64 a)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
	15.9b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 r (sin.f64 b))) 2) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (cbrt.f64 (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))))
	0.5b	(/.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 a) 2) (pow.f64 (sin.f64 b) 2))))

Compiler

Compiled 9006 to 2795 computations (69% saved)

regimes1.5s (13.7%)

Accuracy

Total 0.3b remaining (82.5%)

Threshold costs 0.3b (82.5%)

Counts

301 → 1

Compiler

Compiled 29049 to 17049 computations (41.3% saved)

simplify3.0ms (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

end272.0ms (2.5%)

Compiler: Compiled 544 to 298 computations (45.2% saved)

Details

analyze1.5s (13.2%)

sample4.2s (37.7%)

localize7.0ms (0.1%)

series56.0ms (0.5%)

rewrite100.0ms (0.9%)

prune317.0ms (2.9%)

localize13.0ms (0.1%)

series136.0ms (1.2%)

rewrite85.0ms (0.8%)

prune508.0ms (4.6%)

localize13.0ms (0.1%)

series140.0ms (1.3%)

rewrite84.0ms (0.8%)

prune422.0ms (3.8%)

localize19.0ms (0.2%)

series1.3s (11.4%)

rewrite91.0ms (0.8%)

prune396.0ms (3.6%)

regimes1.5s (13.7%)

simplify3.0ms (0%)

end272.0ms (2.5%)

Profiling