Details

analyze1.7s (9.9%)

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)

sample4.0s (24.1%)

Results

2.5s	3650×	body	1024	valid
612.0ms	1434×	body	512	valid
378.0ms	2360×	body	128	valid
293.0ms	222×	body	2048	valid
180.0ms	590×	body	256	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
2	16	14
3	20	14
4	21	14
5	21	14

prune5.0ms (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

16.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.4b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))

Compiler

Compiled 45 to 28 computations (37.8% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 b)
✓	0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
✓	0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
✓	3.4b	(cos.f64 (+.f64 a b))

series88.0ms (0.5%)

Counts

4 → 56

Calls

4 calls:

49.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
32.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
4.0ms	(cos.f64 (+.f64 a b))
2.0ms	(sin.f64 b)

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
13×	`associate-r_binary64`

Counts

4 → 82

Calls

4 calls:

6.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
3.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
3.0ms	(cos.f64 (+.f64 a b))
1.0ms	(sin.f64 b)

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

757×	`fma-def_binary64`
561×	`associate-/r*_binary64`
281×	`associate-/r/_binary64`
239×	`associate-/l/_binary64`
206×	`associate-r_binary64`

Counts

138 → 187

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	2895
1	667	2747
2	2416	2681
3	4988	2681
4	5029	2681

prune188.0ms (1.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	175	12	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	176	12	188

Error

0.2b

Counts

188 → 12

Alt Table

Status	Error	Program
	32.9b	(.f64 r (/.f64 (sin.f64 b) (.f64 (sqrt.f64 (cos.f64 (+.f64 a b))) (sqrt.f64 (cos.f64 (+.f64 a b))))))
	31.9b	(fma.f64 (/.f64 b (cos.f64 a)) r (/.f64 (.f64 (sin.f64 a) (.f64 b (*.f64 b r))) (pow.f64 (cos.f64 a) 2)))
	16.5b	(.f64 r (/.f64 (sin.f64 b) (cbrt.f64 (.f64 (*.f64 (cos.f64 (+.f64 a b)) (cos.f64 (+.f64 a b))) (cos.f64 (+.f64 a b))))))
	16.4b	(/.f64 (*.f64 (sin.f64 b) r) (cos.f64 (+.f64 a b)))
	16.7b	(.f64 (.f64 r (/.f64 1 (*.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) (cbrt.f64 (cos.f64 (+.f64 a b)))))) (/.f64 (sin.f64 b) (cbrt.f64 (cos.f64 (+.f64 a b)))))
	40.0b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 (sin.f64 b) r) (cos.f64 (+.f64 b a))) 3))
	31.3b	(fma.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r (/.f64 (.f64 (pow.f64 (sin.f64 b) 2) (.f64 a r)) (pow.f64 (cos.f64 b) 2)))
▶	0.3b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
	31.0b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (cos.f64 a) (.f64 b (+.f64 (sin.f64 a) (.f64 (.f64 1/2 (cos.f64 a)) b))))))
	16.4b	(*.f64 r (/.f64 (sin.f64 b) (expm1.f64 (log1p.f64 (cos.f64 (+.f64 a b))))))
	35.5b	(.f64 (sqrt.f64 (.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))) (sqrt.f64 (*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))))
	17.1b	(.f64 (.f64 (cbrt.f64 (.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))) (cbrt.f64 (.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))))) (cbrt.f64 (*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))))

Compiler

Compiled 4327 to 1443 computations (66.7% 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 a) (sin.f64 b)))
✓	0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
✓	0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
✓	0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))

series202.0ms (1.2%)

Counts

4 → 80

Calls

4 calls:

111.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
65.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
16.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
9.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
20×	`associate-r_binary64`
19×	`times-frac_binary64`

Counts

4 → 110

Calls

4 calls:

9.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
6.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
5.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
3.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify145.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

386×	`fma-neg_binary64`
323×	`cancel-sign-sub-inv_binary64`
290×	`associate-r_binary64`
268×	`associate-l_binary64`
198×	`distribute-rgt-neg-in_binary64`

Counts

190 → 216

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	5599
1	871	5281
2	3258	5029
3	4530	5023
4	4971	5023

prune248.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	205	11	216
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	215	13	228

Error

0.0b

Counts

228 → 13

Alt Table

Status	Error	Program
	0.7b	(.f64 r (/.f64 (sin.f64 b) (log.f64 (/.f64 (exp.f64 (.f64 (cos.f64 a) (cos.f64 b))) (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))))
	0.9b	(.f64 (.f64 r (/.f64 1 (.f64 (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))) (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))))) (/.f64 (sin.f64 b) (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
▶	0.3b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))))
	1.3b	(.f64 (.f64 (cbrt.f64 (/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))) (cbrt.f64 (/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1))))) (cbrt.f64 (/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))))
	0.4b	(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
	40.0b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 (sin.f64 b) r) (cos.f64 (+.f64 b a))) 3))
	14.2b	(.f64 r (cbrt.f64 (.f64 (.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))) (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))) (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))))
	0.5b	(.f64 (.f64 r (/.f64 (sin.f64 b) (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 a) (sin.f64 b)) 3)))) (+.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (+.f64 (.f64 (.f64 (sin.f64 a) (sin.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	0.4b	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))
	0.5b	(.f64 r (/.f64 (sin.f64 b) (cbrt.f64 (.f64 (.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))))
	24.8b	(.f64 (.f64 r (/.f64 1 (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))) (/.f64 (sin.f64 b) (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))))
	16.4b	(*.f64 r (/.f64 (sin.f64 b) (expm1.f64 (log1p.f64 (cos.f64 (+.f64 a b))))))

Compiler

Compiled 6805 to 1963 computations (71.2% saved)

localize12.0ms (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 a) (sin.f64 b))))
	0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
✓	0.2b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))))
✓	0.2b	(/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))

series191.0ms (1.1%)

Counts

3 → 84

Calls

3 calls:

112.0ms

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

64.0ms

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

15.0ms

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

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

3 → 73

Calls

3 calls:

5.0ms

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

3.0ms

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

0.0ms

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

simplify132.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

711×	`fma-def_binary64`
566×	`associate-/r*_binary64`
285×	`associate-/r/_binary64`
240×	`associate-/l/_binary64`
199×	`associate-r_binary64`

Counts

157 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	250	4914
1	627	4622
2	2345	4559
3	4948	4558
4	4980	4558

prune247.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	215	4	219
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	219	13	232

Error

0.0b

Counts

232 → 13

Alt Table

Status	Error	Program
	7.8b	(.f64 r (expm1.f64 (log1p.f64 (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))))))
	0.5b	(.f64 r (/.f64 (sin.f64 b) (cbrt.f64 (.f64 (.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))))
	0.9b	(.f64 (/.f64 r (.f64 (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))) (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))) (/.f64 (sin.f64 b) (cbrt.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))))
	1.3b	(.f64 (.f64 (cbrt.f64 (/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))) (cbrt.f64 (/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1))))) (cbrt.f64 (/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))))
▶	0.4b	(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
	0.5b	(.f64 (.f64 r (/.f64 (sin.f64 b) (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 a) (sin.f64 b)) 3)))) (+.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (+.f64 (.f64 (.f64 (sin.f64 a) (sin.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	0.4b	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))
	1.0b	(.f64 r (log1p.f64 (expm1.f64 (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))))))
	24.8b	(.f64 (.f64 r (/.f64 1 (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))) (/.f64 (sin.f64 b) (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))))
	16.4b	(*.f64 r (/.f64 (sin.f64 b) (expm1.f64 (log1p.f64 (cos.f64 (+.f64 a b))))))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))))
	1.0b	(.f64 r (.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))) (cbrt.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))))) (/.f64 (sin.f64 b) (cbrt.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))))))
	14.2b	(.f64 r (cbrt.f64 (.f64 (.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))) (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))) (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))))

Compiler

Compiled 7009 to 1853 computations (73.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1))
✓	0.2b	(/.f64 (sin.f64 b) (cos.f64 b))
✓	0.2b	(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
✓	0.3b	(/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b)))

series395.0ms (2.4%)

Counts

4 → 88

Calls

4 calls:

343.0ms	(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
23.0ms	(-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1))
22.0ms	(/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b)))
7.0ms	(/.f64 (sin.f64 b) (cos.f64 b))

rewrite882.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Rules

1540×	`times-frac_binary64`
1028×	`add-sqr-sqrt_binary64`
923×	`*-un-lft-identity_binary64`
878×	`add-cube-cbrt_binary64`
572×	`prod-diff_binary64`

Counts

4 → 832

Calls

4 calls:

40.0ms	(-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1))
27.0ms	(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
6.0ms	(/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b)))
3.0ms	(/.f64 (sin.f64 b) (cos.f64 b))

simplify1.0s (6.2%)

Algorithm

1×	egg-herbie

Rules

314×	`fma-neg_binary64`
259×	`associate-/l*_binary64`
252×	`fma-udef_binary64`
228×	`associate-r_binary64`
201×	`associate-*l/_binary64`

Counts

920 → 1057

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	715	35477
1	1097	33287
2	4118	29114
3	4710	29113
4	4957	29113
5	4931	29113

prune1.6s (9.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	1052	5	1057
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	1058	12	1070

Error

0.0b

Counts

1070 → 12

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (/.f64 r (-.f64 (.f64 (/.f64 (cos.f64 b) (sin.f64 b)) (cos.f64 a)) (sin.f64 a)))) (cbrt.f64 (/.f64 r (-.f64 (.f64 (/.f64 (cos.f64 b) (sin.f64 b)) (cos.f64 a)) (sin.f64 a))))) (cbrt.f64 (/.f64 r (-.f64 (*.f64 (/.f64 (cos.f64 b) (sin.f64 b)) (cos.f64 a)) (sin.f64 a)))))
	0.4b	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))
	0.7b	(/.f64 r (-.f64 (.f64 (/.f64 1 (/.f64 1 (.f64 (cbrt.f64 (cos.f64 b)) (cbrt.f64 (cos.f64 b))))) (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cbrt.f64 (cos.f64 b))))) (/.f64 (sin.f64 a) 1)))
	0.5b	(.f64 r (/.f64 (sin.f64 b) (cbrt.f64 (.f64 (.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))))
	16.4b	(*.f64 r (/.f64 (sin.f64 b) (expm1.f64 (log1p.f64 (cos.f64 (+.f64 a b))))))
	32.5b	(/.f64 r (-.f64 (/.f64 (cos.f64 a) (*.f64 (sqrt.f64 (sin.f64 b)) (/.f64 (sqrt.f64 (sin.f64 b)) (cos.f64 b)))) (/.f64 (sin.f64 a) 1)))
	0.4b	(/.f64 r (/.f64 (-.f64 (cos.f64 a) (*.f64 (sin.f64 a) (/.f64 (sin.f64 b) (cos.f64 b)))) (/.f64 (sin.f64 b) (cos.f64 b))))
	0.5b	(.f64 (.f64 r (/.f64 (sin.f64 b) (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 a) (sin.f64 b)) 3)))) (+.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (+.f64 (.f64 (.f64 (sin.f64 a) (sin.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	0.7b	(/.f64 r (+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 a)) (cbrt.f64 (cos.f64 a))) (sin.f64 b)) (.f64 (cos.f64 b) (cbrt.f64 (cos.f64 a))) (neg.f64 (sin.f64 a))) 0))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))))
	1.0b	(.f64 r (.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))) (cbrt.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))))) (/.f64 (sin.f64 b) (cbrt.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))))))
	14.2b	(.f64 r (cbrt.f64 (.f64 (.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))) (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))) (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))))

Compiler

Compiled 50802 to 20307 computations (60% saved)

regimes5.3s (31.5%)

Accuracy

Total 0.3b remaining (85.3%)

Threshold costs 0.3b (85.3%)

Counts

655 → 1

Compiler

Compiled 94652 to 55336 computations (41.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`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	23	26
2	31	26
3	36	26
4	38	26
5	38	26

end209.0ms (1.2%)

Compiler: Compiled 445 to 208 computations (53.3% saved)

Details

analyze1.7s (9.9%)

sample4.0s (24.1%)

simplify6.0ms (0%)

prune5.0ms (0%)

localize7.0ms (0%)

series88.0ms (0.5%)

rewrite20.0ms (0.1%)

simplify97.0ms (0.6%)

prune188.0ms (1.1%)

localize12.0ms (0.1%)

series202.0ms (1.2%)

rewrite31.0ms (0.2%)

simplify145.0ms (0.9%)

prune248.0ms (1.5%)

localize12.0ms (0.1%)

series191.0ms (1.1%)

rewrite14.0ms (0.1%)

simplify132.0ms (0.8%)

prune247.0ms (1.5%)

localize12.0ms (0.1%)

series395.0ms (2.4%)

rewrite882.0ms (5.3%)

simplify1.0s (6.2%)

prune1.6s (9.7%)

regimes5.3s (31.5%)

simplify3.0ms (0%)

end209.0ms (1.2%)

Profiling