Details

analyze1.6s (13.4%)

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)

sample4.6s (38.7%)

Results

2.4s	3561×	body	1024	valid
1.1s	2419×	body	128	valid
610.0ms	1445×	body	512	valid
280.0ms	202×	body	2048	valid
193.0ms	629×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify9.0ms (0.1%)

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

14.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.1b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))

Compiler

Compiled 45 to 27 computations (40% saved)

localize8.0ms (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)))
✓	3.9b	(cos.f64 (+.f64 a b))

series58.0ms (0.5%)

Counts

3 → 68

Calls

3 calls:

47.0ms	(/.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))

rewrite104.0ms (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:

100.0ms	(*.f64 r (sin.f64 b))
100.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
100.0ms	(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

simplify63.0ms (0.5%)

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

194 → 164

Iterations

Useful iterations: 2 (0.0ms)

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

prune231.0ms (1.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	149	15	164
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	15	165

Error

0.1b

Counts

165 → 15

Alt Table

Status	Error	Program
	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))))))
	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)) (+.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)))))
	14.8b	(.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)))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.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))))))))
	14.2b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	14.3b	(/.f64 (*.f64 r (sin.f64 b)) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3)))
	14.3b	(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (+.f64 a b))))))
	24.0b	(/.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)))))
	31.7b	(/.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)))))))
	0.4b	(/.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))))))
	14.2b	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a b))))
	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)))))
	29.9b	(fma.f64 1/2 (.f64 (/.f64 (.f64 (sin.f64 b) r) (cos.f64 b)) (.f64 a a)) (fma.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) (.f64 a r) (/.f64 (.f64 (.f64 a (*.f64 a r)) (pow.f64 (sin.f64 b) 3)) (pow.f64 (cos.f64 b) 3)))))

Compiler

Compiled 5077 to 1626 computations (68% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 1 (.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 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)))))
✓	52.4b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series191.0ms (1.6%)

Counts

4 → 108

Calls

4 calls:

139.0ms	(/.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)))))
24.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))
17.0ms	(fma.f64 1 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1))))
9.0ms	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))

rewrite121.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

311×	`log1p-udef_binary64`
310×	`expm1-udef_binary64`
195×	`add-sqr-sqrt_binary64`
180×	`log1p-expm1-u_binary64`
180×	`expm1-log1p-u_binary64`

Counts

4 → 114

Calls

4 calls:

118.0ms	(fma.f64 1 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1))))
118.0ms	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))
118.0ms	(/.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)))))
118.0ms	(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	19	94
1	382	52
2	4492	52
3	5000	52
4	5326	52
0	0	0
1	0	0

simplify80.0ms (0.7%)

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

222 → 163

Iterations

Useful iterations: 3 (0.0ms)

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

prune448.0ms (3.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	197	5	202
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	201	16	217

Error

0.0b

Counts

217 → 16

Alt Table

Status	Error	Program
	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))))))
	14.8b	(.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)))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.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))))))))
	14.2b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	14.3b	(/.f64 (*.f64 r (sin.f64 b)) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3)))
	14.2b	(.f64 (/.f64 (.f64 (sin.f64 b) r) (+.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3) (pow.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) 0) 3))) (+.f64 (pow.f64 (cos.f64 (+.f64 a b)) 2) (.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) 0) (-.f64 (.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 0) (cos.f64 (+.f64 a b))))))
	14.3b	(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (+.f64 a b))))))
	24.0b	(/.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)))))
	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) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))))
	29.9b	(fma.f64 1/2 (.f64 (/.f64 (.f64 (sin.f64 b) r) (cos.f64 b)) (.f64 a a)) (fma.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) (.f64 a r) (/.f64 (.f64 (.f64 a (*.f64 a r)) (pow.f64 (sin.f64 b) 3)) (pow.f64 (cos.f64 b) 3)))))
	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))))))
▶	0.3b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.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)))))
	0.3b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.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 (cbrt.f64 (.f64 (pow.f64 (sin.f64 b) 3) (pow.f64 (sin.f64 a) 3))))) (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 1 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (log.f64 (pow.f64 (exp.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)))))

Compiler

Compiled 8270 to 3399 computations (58.9% saved)

localize23.0ms (0.2%)

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 1 (.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)))))
	52.4b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series150.0ms (1.3%)

Counts

2 → 52

Calls

2 calls:

140.0ms

(/.f64 (*.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (*.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)))))

9.0ms

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

rewrite74.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

767×	`prod-diff_binary64`
207×	`add-sqr-sqrt_binary64`
196×	`expm1-log1p-u_binary64`
195×	`log1p-expm1-u_binary64`
189×	`add-cbrt-cube_binary64`

Counts

2 → 65

Calls

2 calls:

73.0ms

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

73.0ms

(/.f64 (*.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (*.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	22	56
1	407	37
2	4384	22
3	5518	22
0	0	0
1	0	0

simplify82.0ms (0.7%)

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

117 → 98

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

prune370.0ms (3.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	2	13	15
Picked	0	1	1
Done	0	0	0
Total	163	16	179

Error

0.0b

Counts

179 → 16

Alt Table

Status	Error	Program
	14.7b	(.f64 (/.f64 (.f64 r (sin.f64 b)) (-.f64 (pow.f64 (cos.f64 (-.f64 b a)) 2) (pow.f64 (.f64 (sin.f64 a) (+.f64 (sin.f64 b) (sin.f64 b))) 2))) (-.f64 (cos.f64 (-.f64 b a)) (.f64 (sin.f64 a) (+.f64 (sin.f64 b) (sin.f64 b)))))
	29.9b	(fma.f64 1/2 (.f64 (/.f64 (.f64 (sin.f64 b) r) (cos.f64 b)) (.f64 a a)) (fma.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) (.f64 r a) (.f64 (pow.f64 (/.f64 (sin.f64 b) (cos.f64 b)) 3) (.f64 r (*.f64 a a))))))
	14.8b	(.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)))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.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))))))))
	14.2b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	14.3b	(/.f64 (*.f64 r (sin.f64 b)) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3)))
	14.2b	(.f64 (/.f64 (.f64 (sin.f64 b) r) (+.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3) (pow.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) 0) 3))) (+.f64 (pow.f64 (cos.f64 (+.f64 a b)) 2) (.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) 0) (-.f64 (.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 0) (cos.f64 (+.f64 a b))))))
	14.3b	(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (+.f64 a b))))))
	24.0b	(/.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)))))
	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))))))
	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))))))
✓	0.3b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.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)))))
▶	0.3b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.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 (cbrt.f64 (.f64 (pow.f64 (sin.f64 b) 3) (pow.f64 (sin.f64 a) 3))))) (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 1 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (log.f64 (pow.f64 (exp.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 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) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))))

Compiler

Compiled 6752 to 2570 computations (61.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series128.0ms (1.1%)

Counts

2 → 60

Calls

2 calls:

113.0ms	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))))
15.0ms	(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))

rewrite142.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

779×	`prod-diff_binary64`
400×	`egg-rr`
244×	`log1p-udef_binary64`
146×	`add-sqr-sqrt_binary64`
134×	`log1p-expm1-u_binary64`

Counts

2 → 400

Calls

2 calls:

128.0ms	(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))
128.0ms	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	276	20
2	3413	20
3	5310	20
0	0	0
1	0	0

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
664×	`associate-/l*_binary64`
486×	`associate-l_binary64`
460×	`fma-def_binary64`
310×	`associate-/r*_binary64`

Counts

460 → 430

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1643
1	341	1641
2	1190	1603
3	5479	1603

prune921.0ms (7.7%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	491	6	497
Fresh	7	7	14
Picked	0	1	1
Done	0	1	1
Total	498	15	513

Error

0.0b

Counts

513 → 15

Alt Table

Status	Error	Program
	29.9b	(fma.f64 1/2 (.f64 (/.f64 (.f64 (sin.f64 b) r) (cos.f64 b)) (.f64 a a)) (fma.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) (.f64 r a) (.f64 (pow.f64 (/.f64 (sin.f64 b) (cos.f64 b)) 3) (.f64 r (*.f64 a a))))))
	14.8b	(.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)))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.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))))))))
✓	0.3b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 1 (.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)))))
	31.8b	(/.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 (sqrt.f64 (sin.f64 b)) (sin.f64 a)) (sqrt.f64 (sin.f64 b))))) (fma.f64 (neg.f64 (.f64 (sqrt.f64 (sin.f64 b)) (sin.f64 a))) (sqrt.f64 (sin.f64 b)) (.f64 (*.f64 (sqrt.f64 (sin.f64 b)) (sin.f64 a)) (sqrt.f64 (sin.f64 b))))))
	14.2b	(.f64 (sin.f64 b) (.f64 r (/.f64 1 (cos.f64 (-.f64 b a)))))
	31.0b	(/.f64 (pow.f64 (sqrt.f64 (.f64 r (sin.f64 b))) 2) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))))
	14.3b	(/.f64 (*.f64 r (sin.f64 b)) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3)))
	14.2b	(.f64 (/.f64 (.f64 (sin.f64 b) r) (+.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3) (pow.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) 0) 3))) (+.f64 (pow.f64 (cos.f64 (+.f64 a b)) 2) (.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) 0) (-.f64 (.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 0) (cos.f64 (+.f64 a b))))))
	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)))))
	14.3b	(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (exp.f64 (cos.f64 (-.f64 b 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))))))
	14.6b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (sqrt.f64 (cos.f64 a)) (.f64 (sqrt.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)))))
✓	0.3b	(/.f64 (.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.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 (log.f64 (pow.f64 (exp.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)))))

Compiler

Compiled 19371 to 4086 computations (78.9% saved)

regimes2.1s (17.6%)

Accuracy

Total 0.3b remaining (74.6%)

Threshold costs 0.3b (74.6%)

Counts

382 → 1

Compiler

Compiled 47320 to 25628 computations (45.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-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	22	53
1	33	53
2	37	53
3	39	53
4	38	53

end294.0ms (2.5%)

Compiler: Compiled 657 to 332 computations (49.5% saved)

Details

analyze1.6s (13.4%)

sample4.6s (38.7%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series58.0ms (0.5%)

rewrite104.0ms (0.9%)

simplify63.0ms (0.5%)

prune231.0ms (1.9%)

localize18.0ms (0.2%)

series191.0ms (1.6%)

rewrite121.0ms (1%)

simplify80.0ms (0.7%)

prune448.0ms (3.8%)

localize23.0ms (0.2%)

series150.0ms (1.3%)

rewrite74.0ms (0.6%)

simplify82.0ms (0.7%)

prune370.0ms (3.1%)

localize12.0ms (0.1%)

series128.0ms (1.1%)

rewrite142.0ms (1.2%)

simplify65.0ms (0.5%)

prune921.0ms (7.7%)

regimes2.1s (17.6%)

simplify4.0ms (0%)

end294.0ms (2.5%)

Profiling