Details

analyze1.5s (7.2%)

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)

sample4.5s (21.8%)

Results

3.0s	3591×	body	1024	valid
564.0ms	1365×	body	512	valid
404.0ms	2453×	body	128	valid
303.0ms	214×	body	2048	valid
199.0ms	633×	body	256	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
2	17	14
3	20	14
4	21	14
5	21	14

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

15.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.1b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))

Compiler

Compiled 45 to 27 computations (40% saved)

localize7.0ms (0%)

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)))
✓	2.7b	(cos.f64 (+.f64 a b))

series59.0ms (0.3%)

Counts

3 → 68

Calls

3 calls:

46.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
8.0ms	(*.f64 r (sin.f64 b))
5.0ms	(cos.f64 (+.f64 a b))

rewrite102.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 129

Calls

3 calls:

99.0ms	(*.f64 r (sin.f64 b))
99.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
99.0ms	(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

simplify83.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
659×	`associate-/l*_binary64`
533×	`fma-def_binary64`
310×	`associate-/r*_binary64`
177×	`fma-neg_binary64`

Counts

197 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1221
1	387	1211
2	1352	1163
3	4913	1163
4	4972	1163

prune251.0ms (1.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	151	16	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	152	16	168

Error

0.1b

Counts

168 → 16

Alt Table

Status	Error	Program
	15.1b	(/.f64 (*.f64 r (sin.f64 b)) (log1p.f64 (expm1.f64 (cos.f64 (+.f64 a b)))))
	15.3b	(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (+.f64 a b)))) 1))
	0.9b	(/.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) (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))))))
	15.4b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (/.f64 (.f64 r (sin.f64 b)) (cbrt.f64 (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)))))))
	32.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.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 r (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))))))
	15.6b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	15.2b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	30.3b	(*.f64 (/.f64 r (sqrt.f64 (cos.f64 (+.f64 a b)))) (/.f64 (sin.f64 b) (sqrt.f64 (cos.f64 (+.f64 a b)))))
	0.3b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.8b	(/.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)))))
	15.1b	(*.f64 (/.f64 r 1) (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
	36.5b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b))) 3))
	32.4b	(/.f64 (.f64 r (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)))))))
▶	0.3b	(/.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)))))

Compiler

Compiled 4968 to 1580 computations (68.2% saved)

localize19.0ms (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) (.f64 (sin.f64 a) 1))))
✓	0.2b	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))
✓	0.2b	(/.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)))))
✓	49.0b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series192.0ms (0.9%)

Counts

4 → 108

Calls

4 calls:

140.0ms	(/.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)))))
26.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))
15.0ms	(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))))
10.0ms	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))

rewrite121.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

401×	`fma-neg_binary64`
288×	`expm1-udef_binary64`
288×	`log1p-udef_binary64`
180×	`add-sqr-sqrt_binary64`
166×	`log1p-expm1-u_binary64`

Counts

4 → 122

Calls

4 calls:

117.0ms	(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))))
117.0ms	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))
117.0ms	(/.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)))))
117.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	90
1	356	72
2	4103	72
3	4959	72
4	5301	72
0	0	0
1	0	0

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
664×	`associate-/l*_binary64`
607×	`fma-def_binary64`
273×	`fma-neg_binary64`
240×	`cancel-sign-sub-inv_binary64`

Counts

230 → 170

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	1999
1	437	1989
2	1486	1927
3	4980	1923
4	5088	1923

prune1.1s (5.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	205	4	209
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	208	17	225

Error

0.0b

Counts

225 → 17

Alt Table

Status	Error	Program
	15.1b	(/.f64 (*.f64 r (sin.f64 b)) (log1p.f64 (expm1.f64 (cos.f64 (+.f64 a b)))))
	15.3b	(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (+.f64 a b)))) 1))
	0.8b	(/.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)))))
▶	0.3b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (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)))))
	0.9b	(/.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) (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))))))
	0.3b	(/.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) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))
	15.4b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (/.f64 (.f64 r (sin.f64 b)) (cbrt.f64 (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)))))))
	32.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.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 r (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))))))
	15.6b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	15.2b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	30.3b	(*.f64 (/.f64 r (sqrt.f64 (cos.f64 (+.f64 a b)))) (/.f64 (sin.f64 b) (sqrt.f64 (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 (exp.f64 (log1p.f64 (.f64 (sin.f64 b) (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)))))
	15.1b	(*.f64 (/.f64 r 1) (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
	36.5b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b))) 3))
	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) (pow.f64 (cbrt.f64 (*.f64 (sin.f64 b) (sin.f64 a))) 3))))

Compiler

Compiled 8615 to 3284 computations (61.9% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))
✓	0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
✓	0.2b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (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)))))
	49.0b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series221.0ms (1.1%)

Counts

2 → 52

Calls

2 calls:

210.0ms

(/.f64 (*.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (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)))))

10.0ms

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

rewrite89.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

312×	`expm1-udef_binary64`
312×	`log1p-udef_binary64`
195×	`add-sqr-sqrt_binary64`
183×	`expm1-log1p-u_binary64`
182×	`log1p-expm1-u_binary64`

Counts

2 → 73

Calls

2 calls:

86.0ms

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

86.0ms

(/.f64 (*.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (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)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	54
1	382	47
2	4445	47
3	5297	47
0	0	0
1	0	0

simplify84.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
664×	`associate-/l*_binary64`
499×	`fma-def_binary64`
310×	`associate-/r*_binary64`
184×	`fma-neg_binary64`

Counts

125 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1479
1	379	1469
2	1298	1409
3	4862	1399
4	4984	1399
5	4977	1399

prune400.0ms (1.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	173	17	190

Error

0.0b

Counts

190 → 17

Alt Table

Status	Error	Program
	15.1b	(/.f64 (*.f64 r (sin.f64 b)) (log1p.f64 (expm1.f64 (cos.f64 (+.f64 a b)))))
	15.3b	(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (+.f64 a b)))) 1))
	0.8b	(/.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)))))
✓	0.3b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (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)))))
	0.9b	(/.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) (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))))))
▶	0.3b	(/.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) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))
	15.4b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (/.f64 (.f64 r (sin.f64 b)) (cbrt.f64 (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)))))))
	32.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.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 r (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))))))
	15.6b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	15.2b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	30.3b	(*.f64 (/.f64 r (sqrt.f64 (cos.f64 (+.f64 a b)))) (/.f64 (sin.f64 b) (sqrt.f64 (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 (exp.f64 (log1p.f64 (.f64 (sin.f64 b) (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)))))
	15.1b	(*.f64 (/.f64 r 1) (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
	36.5b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b))) 3))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a)))))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (pow.f64 (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a))) 3))))

Compiler

Compiled 7457 to 2379 computations (68.1% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
✓	0.2b	(/.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) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))
✓	3.1b	(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
✓	18.5b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a))))))

series10.1s (49.3%)

Counts

3 → 84

Calls

3 calls:

9.1s

(fma.f64 (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) 1) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))

720.0ms

(/.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) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))

358.0ms

(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))

rewrite80.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

620×	`prod-diff_binary64`
208×	`add-sqr-sqrt_binary64`
195×	`log1p-expm1-u_binary64`
195×	`expm1-log1p-u_binary64`
191×	`add-log-exp_binary64`

Counts

3 → 106

Calls

3 calls:

78.0ms

(/.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) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))

78.0ms

(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))

78.0ms

(fma.f64 (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) 1) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	72
1	410	56
2	4455	43
3	5426	43
0	0	0
1	0	0

simplify66.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
664×	`associate-/l*_binary64`
502×	`fma-def_binary64`
310×	`associate-/r*_binary64`
190×	`fma-neg_binary64`

Counts

190 → 139

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	1567
1	384	1557
2	1309	1497
3	4885	1493
4	4958	1493

prune370.0ms (1.8%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	179	4	183
Fresh	3	12	15
Picked	0	1	1
Done	0	1	1
Total	182	18	200

Error

0.0b

Counts

200 → 18

Alt Table

Status	Error	Program
	15.1b	(/.f64 (*.f64 r (sin.f64 b)) (log1p.f64 (expm1.f64 (cos.f64 (+.f64 a b)))))
	15.3b	(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (+.f64 a b)))) 1))
	0.8b	(/.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)))))
✓	0.3b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (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 (.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 (log.f64 (+.f64 1 (pow.f64 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a))) 3))) (log.f64 (+.f64 1 (-.f64 (pow.f64 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a))) 2) (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))))
	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 (log.f64 (sqrt.f64 (exp.f64 (.f64 (sin.f64 b) (sin.f64 a))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 (sin.f64 b) (sin.f64 a)))))))))
	15.1b	(*.f64 (/.f64 r 1) (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
✓	0.3b	(/.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) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))
	15.4b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (/.f64 (.f64 r (sin.f64 b)) (cbrt.f64 (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)))))))
	32.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.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 r (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))))))
	15.6b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	15.2b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	1.9b	(/.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 (log.f64 (-.f64 1 (pow.f64 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a))) 2))) (log.f64 (-.f64 1 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a)))))))))
	36.5b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b))) 3))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a)))))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (pow.f64 (cbrt.f64 (.f64 (sin.f64 b) (sin.f64 a))) 3))))
	14.9b	(.f64 (/.f64 r (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a)))) (sin.f64 b))

Compiler

Compiled 7131 to 2776 computations (61.1% saved)

regimes836.0ms (4.1%)

Accuracy

Total 0.2b remaining (75.3%)

Threshold costs 0.2b (75.3%)

Counts

184 → 1

Compiler

Compiled 21799 to 12953 computations (40.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	54
1	31	54
2	35	54
3	37	54
4	36	54

end303.0ms (1.5%)

Compiler: Compiled 661 to 357 computations (46% saved)

Details

analyze1.5s (7.2%)

sample4.5s (21.8%)

simplify8.0ms (0%)

prune2.0ms (0%)

localize7.0ms (0%)

series59.0ms (0.3%)

rewrite102.0ms (0.5%)

simplify83.0ms (0.4%)

prune251.0ms (1.2%)

localize19.0ms (0.1%)

series192.0ms (0.9%)

rewrite121.0ms (0.6%)

simplify77.0ms (0.4%)

prune1.1s (5.2%)

localize21.0ms (0.1%)

series221.0ms (1.1%)

rewrite89.0ms (0.4%)

simplify84.0ms (0.4%)

prune400.0ms (1.9%)

localize24.0ms (0.1%)

series10.1s (49.3%)

rewrite80.0ms (0.4%)

simplify66.0ms (0.3%)

prune370.0ms (1.8%)

regimes836.0ms (4.1%)

simplify4.0ms (0%)

end303.0ms (1.5%)

Profiling