Details

analyze2.3s (16.5%)

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)

sample4.7s (33.3%)

Results

2.9s	3582×	body	1024	valid
677.0ms	1387×	body	512	valid
583.0ms	2427×	body	128	valid
338.0ms	216×	body	2048	valid
193.0ms	644×	body	256	valid
1.0ms	2×	body	1024	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`
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

14.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.5b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))

Compiler

Compiled 45 to 27 computations (40% 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)))
✓	3.7b	(cos.f64 (+.f64 a b))

series58.0ms (0.4%)

Counts

3 → 68

Calls

3 calls:

46.0ms	(/.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))

rewrite228.0ms (1.6%)

Algorithm

3×	egg-rewrite

Rules

60×	`egg`
49×	`egg`
43×	`egg`

Counts

3 → 152

Calls

3 calls:

92.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
84.0ms	(*.f64 r (sin.f64 b))
49.0ms	(cos.f64 (+.f64 a b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	115	6
2	1548	6
3	5067	6
0	9	14
1	200	14
2	2799	14
3	4792	14
4	5009	14
0	5	6
1	97	6
2	1114	6
3	4736	6
4	6242	6

simplify76.0ms (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

220 → 188

Iterations

Useful iterations: 2 (0.0ms)

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

prune388.0ms (2.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	175	13	188
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	176	13	189

Error

0.0b

Counts

189 → 13

Alt Table

Status	Error	Program
	34.3b	(.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (/.f64 1 (cos.f64 (+.f64 b a)))))
	43.1b	(/.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 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sqrt.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (sqrt.f64 (.f64 (sin.f64 a) (sin.f64 b))) (*.f64 (sin.f64 a) (sin.f64 b)))))
▶	0.3b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	29.1b	(fma.f64 (/.f64 b (cos.f64 a)) r (/.f64 (.f64 (sin.f64 a) (.f64 b (*.f64 b r))) (pow.f64 (cos.f64 a) 2)))
	15.2b	(/.f64 1 (/.f64 (cos.f64 (+.f64 b a)) (*.f64 r (sin.f64 b))))
	0.4b	(/.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 a) (sin.f64 b))) (.f64 (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b))) (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b))))))) (fma.f64 (neg.f64 (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (.f64 (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b))) (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (.f64 (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b))) (.f64 (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b))) (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b))))))))
	14.5b	(/.f64 r (/.f64 (cos.f64 (+.f64 b a)) (sin.f64 b)))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.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 (-.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)))))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b))) (.f64 (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b))) (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b))))))) (fma.f64 (neg.f64 (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (.f64 (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b))) (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (.f64 (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b))) (.f64 (cbrt.f64 (.f64 (sin.f64 a) (sin.f64 b))) (cbrt.f64 (*.f64 (sin.f64 a) (sin.f64 b))))))))
	0.8b	(/.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 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	29.0b	(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)))
	14.7b	(*.f64 (/.f64 r (cos.f64 (+.f64 b a))) (sin.f64 b))

Compiler

Compiled 4940 to 1451 computations (70.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 r (sin.f64 b))
✓	0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
✓	0.2b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
✓	51.8b	(fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))

series184.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

131.0ms

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

43.0ms

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

10.0ms

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

rewrite215.0ms (1.5%)

Algorithm

3×	egg-rewrite

Rules

62×	`egg`
35×	`egg`
24×	`egg`

Counts

3 → 121

Calls

3 calls:

82.0ms

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

80.0ms

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

50.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	167	13
2	1855	13
3	5734	13
0	16	46
1	348	29
2	4188	29
3	4968	29
0	6	8
1	123	8
2	1544	8
3	4889	8
4	5061	8

simplify95.0ms (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

193 → 151

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	131	1471
1	380	1461
2	1298	1401
3	4862	1391
4	4984	1391
5	4977	1391

prune593.0ms (4.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	245	7	252
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	250	15	265

Error

0.0b

Counts

265 → 15

Alt Table

Status	Error	Program
	14.5b	(/.f64 r (/.f64 (cos.f64 (+.f64 b a)) (sin.f64 b)))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.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)))))
▶	0.3b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))))
	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 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)))))))
	1.2b	(/.f64 (pow.f64 (cbrt.f64 (.f64 r (sin.f64 b))) 3) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	14.7b	(*.f64 (/.f64 r (cos.f64 (+.f64 b a))) (sin.f64 b))
	34.2b	(/.f64 (cbrt.f64 (pow.f64 (.f64 r (sin.f64 b)) 3)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 a)) 2) (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b))))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 a) (sin.f64 b)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 a) (sin.f64 b)))) 1))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 a) (sin.f64 b)))) 1))))
	34.3b	(.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (/.f64 1 (cos.f64 (+.f64 b a)))))
	0.8b	(/.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 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	15.2b	(/.f64 1 (/.f64 (cos.f64 (+.f64 b a)) (*.f64 r (sin.f64 b))))
	27.1b	(/.f64 (pow.f64 (sqrt.f64 (.f64 r (sin.f64 b))) 2) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	29.0b	(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)))

Compiler

Compiled 9114 to 2196 computations (75.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))))
✓	0.3b	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)
✓	27.6b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))
✓	51.8b	(fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))

series220.0ms (1.6%)

Counts

4 → 108

Calls

4 calls:

154.0ms	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))))
32.0ms	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)
25.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))
9.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))

rewrite274.0ms (1.9%)

Algorithm

4×	egg-rewrite

Rules

62×	`egg`
39×	`egg`
34×	`egg`
24×	`egg`

Counts

4 → 159

Calls

4 calls:

117.0ms	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))))
54.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))
49.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))
48.0ms	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	216	13
2	2314	13
3	5332	13
0	9	8
1	172	8
2	2005	8
3	5261	8
0	8	11
1	170	11
2	1965	11
3	5178	11
0	19	46
1	396	39
2	4446	39
3	4986	39
4	5270	39

simplify112.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

842×	`fma-def_binary64`
833×	`times-frac_binary64`
340×	`fma-neg_binary64`
301×	`cancel-sign-sub-inv_binary64`
192×	`unswap-sqr_binary64`

Counts

267 → 205

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	163	2079
1	485	2061
2	1818	2029
3	4740	2017
4	4991	2013
5	4953	2013

prune349.0ms (2.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	205	15	220

Error

0.0b

Counts

220 → 15

Alt Table

Status	Error	Program
	14.5b	(/.f64 r (/.f64 (cos.f64 (+.f64 b a)) (sin.f64 b)))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.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)))))
✓	0.3b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))))
	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 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)))))))
	1.2b	(/.f64 (pow.f64 (cbrt.f64 (.f64 r (sin.f64 b))) 3) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	14.7b	(*.f64 (/.f64 r (cos.f64 (+.f64 b a))) (sin.f64 b))
	34.2b	(/.f64 (cbrt.f64 (pow.f64 (.f64 r (sin.f64 b)) 3)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 a)) 2) (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b))))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 a) (sin.f64 b)))))
▶	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 a) (sin.f64 b)))) 1))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 a) (sin.f64 b)))) 1))))
	34.3b	(.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (/.f64 1 (cos.f64 (+.f64 b a)))))
	0.8b	(/.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 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	15.2b	(/.f64 1 (/.f64 (cos.f64 (+.f64 b a)) (*.f64 r (sin.f64 b))))
	27.1b	(/.f64 (pow.f64 (sqrt.f64 (.f64 r (sin.f64 b))) 2) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	29.0b	(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)))

Compiler

Compiled 8240 to 2120 computations (74.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
✓	0.2b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 a) (sin.f64 b)))) 1))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
✓	2.4b	(-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 a) (sin.f64 b)))) 1)
	51.8b	(fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))

series1.6s (11.4%)

Counts

2 → 60

Calls

2 calls:

1.1s

(/.f64 (*.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 a) (sin.f64 b)))) 1))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))

551.0ms

(-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 a) (sin.f64 b)))) 1)

rewrite154.0ms (1.1%)

Algorithm

2×	egg-rewrite

Rules

56×	`egg`
55×	`egg`

Counts

2 → 111

Calls

2 calls:

87.0ms

(/.f64 (*.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 a) (sin.f64 b)))) 1))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))

64.0ms

(-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 a) (sin.f64 b)))) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	8
1	185	8
2	2213	8
3	6459	8
0	20	46
1	404	39
2	4430	24
3	5674	24

simplify102.0ms (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

171 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1543
1	379	1533
2	1298	1473
3	4862	1463
4	4984	1463
5	4977	1463

prune456.0ms (3.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	263	1	264
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	265	14	279

Error

0.0b

Counts

279 → 14

Alt Table

Status	Error	Program
	15.2b	(/.f64 1 (/.f64 (cos.f64 (+.f64 b a)) (*.f64 r (sin.f64 b))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 a) (sin.f64 b)) 3)))) 1))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	14.5b	(/.f64 r (/.f64 (cos.f64 (+.f64 b a)) (sin.f64 b)))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.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)))))
✓	0.3b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))))
	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 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)))))))
	1.2b	(/.f64 (pow.f64 (cbrt.f64 (.f64 r (sin.f64 b))) 3) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	14.7b	(*.f64 (/.f64 r (cos.f64 (+.f64 b a))) (sin.f64 b))
	34.2b	(/.f64 (cbrt.f64 (pow.f64 (.f64 r (sin.f64 b)) 3)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 a) (sin.f64 b)))) 1))))
	34.3b	(.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (/.f64 1 (cos.f64 (+.f64 b a)))))
	0.8b	(/.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 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	27.1b	(/.f64 (pow.f64 (sqrt.f64 (.f64 r (sin.f64 b))) 2) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 a) (sin.f64 b)))))
	29.0b	(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)))

Compiler

Compiled 9653 to 2865 computations (70.3% saved)

regimes1.7s (11.7%)

Accuracy

Total 0.2b remaining (77.1%)

Threshold costs 0.2b (77.1%)

Counts

314 → 1

Compiler

Compiled 36692 to 20042 computations (45.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	60
1	32	60
2	40	60
3	45	58
4	48	58
5	49	58
6	46	58

end257.0ms (1.8%)

Compiler: Compiled 515 to 261 computations (49.3% saved)

Details

analyze2.3s (16.5%)

sample4.7s (33.3%)

simplify6.0ms (0%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series58.0ms (0.4%)

rewrite228.0ms (1.6%)

simplify76.0ms (0.5%)

prune388.0ms (2.7%)

localize17.0ms (0.1%)

series184.0ms (1.3%)

rewrite215.0ms (1.5%)

simplify95.0ms (0.7%)

prune593.0ms (4.2%)

localize18.0ms (0.1%)

series220.0ms (1.6%)

rewrite274.0ms (1.9%)

simplify112.0ms (0.8%)

prune349.0ms (2.5%)

localize21.0ms (0.1%)

series1.6s (11.4%)

rewrite154.0ms (1.1%)

simplify102.0ms (0.7%)

prune456.0ms (3.2%)

regimes1.7s (11.7%)

simplify4.0ms (0%)

end257.0ms (1.8%)

Profiling