Details

analyze2.2s (7.5%)

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)

sample4.4s (15%)

Results

2.8s	3582×	body	1024	valid
654.0ms	1387×	body	512	valid
403.0ms	2427×	body	128	valid
306.0ms	216×	body	2048	valid
224.0ms	644×	body	256	valid
1.0ms	2×	body	1024	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

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%)

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))

series57.0ms (0.2%)

Counts

3 → 68

Calls

3 calls:

45.0ms	(/.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))

rewrite136.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

126× egg-rr

Counts

3 → 126

Calls

2 calls:

133.0ms	((cos.f64 (+.f64 a b)) (/.f64 (.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b))) (.f64 r (sin.f64 b)))
0.0ms	()

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

simplify67.0ms (0.2%)

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

prune226.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	152	12	164
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	12	165

Error

0.0b

Counts

165 → 12

Alt Table

Status	Error	Program
	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))))))
	14.7b	(*.f64 (/.f64 r (cos.f64 (+.f64 a b))) (sin.f64 b))
	14.5b	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a 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)))
	14.5b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	26.2b	(/.f64 (.f64 r (sin.f64 b)) (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) (sin.f64 a)))))
	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 (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)))))
	15.2b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (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 a b)))))
	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)))))
	0.4b	(/.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 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 4727 to 1446 computations (69.4% saved)

localize18.0ms (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 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)))))
✓	51.8b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series163.0ms (0.6%)

Counts

3 → 84

Calls

3 calls:

130.0ms

(/.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)))))

24.0ms

(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) (*.f64 (sin.f64 a) 1))

rewrite127.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

94× egg-rr

Counts

3 → 94

Calls

2 calls:

124.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	72
1	356	56
2	4103	56
3	4959	56
4	5301	56
0	0	0
1	0	0

simplify89.0ms (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

178 → 129

Iterations

Useful iterations: 3 (0.0ms)

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

prune349.0ms (1.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	187	5	192
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	189	15	204

Error

0.0b

Counts

204 → 15

Alt Table

Status	Error	Program
	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))))))
	14.7b	(*.f64 (/.f64 r (cos.f64 (+.f64 a b))) (sin.f64 b))
	14.5b	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a b))))
	27.1b	(/.f64 (pow.f64 (sqrt.f64 (.f64 r (sin.f64 b))) 2) (+.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)))))
	14.5b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	41.9b	(/.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 b) 3) (pow.f64 r 3))) (+.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)))))
	15.2b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	26.2b	(/.f64 (.f64 r (sin.f64 b)) (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) (sin.f64 a)))))
	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 (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) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 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) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))))
	1.2b	(/.f64 (pow.f64 (cbrt.f64 (.f64 r (sin.f64 b))) 3) (+.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)))))
	34.3b	(.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (/.f64 1 (cos.f64 (+.f64 a b)))))
	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)))))
	0.4b	(/.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 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 8047 to 3199 computations (60.2% saved)

localize22.0ms (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 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) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)))))
✓	0.3b	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)
✓	27.6b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))
✓	51.8b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)))

series256.0ms (0.9%)

Counts

4 → 108

Calls

4 calls:

190.0ms	(/.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) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)))))
29.0ms	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)
26.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)))
10.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))

rewrite94.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

147× egg-rr

Counts

4 → 147

Calls

2 calls:

84.0ms

((fma.f64 (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) 1) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)) (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3) (/.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) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	83
1	414	67
2	4532	67
3	4932	67
0	0	0
1	0	0

simplify80.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

839×	`fma-def_binary64`
833×	`times-frac_binary64`
334×	`fma-neg_binary64`
297×	`cancel-sign-sub-inv_binary64`
192×	`unswap-sqr_binary64`

Counts

255 → 195

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	2079
1	481	2061
2	1807	2029
3	4721	2017
4	5049	2017

prune349.0ms (1.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	195	15	210

Error

0.0b

Counts

210 → 15

Alt Table

Status	Error	Program
	14.7b	(*.f64 (/.f64 r (cos.f64 (+.f64 a b))) (sin.f64 b))
	14.5b	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a b))))
	27.1b	(/.f64 (pow.f64 (sqrt.f64 (.f64 r (sin.f64 b))) 2) (+.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)))))
	1.0b	(/.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) (cbrt.f64 (log.f64 (exp.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)))))))
	14.5b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	41.9b	(/.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 b) 3) (pow.f64 r 3))) (+.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)))))
	15.2b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	26.2b	(/.f64 (.f64 r (sin.f64 b)) (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) (sin.f64 a)))))
	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 (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) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 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) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))))
	1.2b	(/.f64 (pow.f64 (cbrt.f64 (.f64 r (sin.f64 b))) 3) (+.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)))))
	34.3b	(.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (/.f64 1 (cos.f64 (+.f64 a b)))))
	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)))))
	0.4b	(/.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 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 8423 to 3321 computations (60.6% saved)

localize22.0ms (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 (.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 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))))
✓	2.4b	(log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a)))
✓	16.5b	(fma.f64 (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) 1) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))

series18.8s (64.6%)

Counts

3 → 84

Calls

3 calls:

16.4s

(fma.f64 (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) 1) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))

1.6s

(/.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 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))))

825.0ms

(log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a)))

rewrite84.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

119× egg-rr

Counts

3 → 119

Calls

2 calls:

80.0ms

((fma.f64 (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) 1) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a)))) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))) (/.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 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a)))))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	72
1	395	56
2	4522	56
3	4949	56
0	0	0
1	0	0

simplify73.0ms (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

203 → 152

Iterations

Useful iterations: 3 (0.0ms)

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

prune277.0ms (1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	191	15	206

Error

0.0b

Counts

206 → 15

Alt Table

Status	Error	Program
	14.7b	(*.f64 (/.f64 r (cos.f64 (+.f64 a b))) (sin.f64 b))
	14.5b	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a b))))
	27.1b	(/.f64 (pow.f64 (sqrt.f64 (.f64 r (sin.f64 b))) 2) (+.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)))))
	1.0b	(/.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) (cbrt.f64 (log.f64 (exp.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)))))))
	14.5b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	41.9b	(/.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 b) 3) (pow.f64 r 3))) (+.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)))))
	15.2b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	26.2b	(/.f64 (.f64 r (sin.f64 b)) (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) (sin.f64 a)))))
	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 (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) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 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) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))))
	1.2b	(/.f64 (pow.f64 (cbrt.f64 (.f64 r (sin.f64 b))) 3) (+.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)))))
	34.3b	(.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (.f64 (sqrt.f64 (.f64 r (sin.f64 b))) (/.f64 1 (cos.f64 (+.f64 a b)))))
	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)))))
	0.4b	(/.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 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 7521 to 2702 computations (64.1% saved)

regimes993.0ms (3.4%)

Accuracy

Total 0.2b remaining (76.8%)

Threshold costs 0.2b (76.8%)

Counts

197 → 1

Compiler

Compiled 23583 to 13907 computations (41% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`distribute-rgt-neg-in_binary64`
3×	`distribute-lft-neg-in_binary64`
3×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	32	46
2	44	46
3	47	46
4	48	46
5	46	46

end267.0ms (0.9%)

Compiler: Compiled 570 to 296 computations (48.1% saved)

Details

analyze2.2s (7.5%)

sample4.4s (15%)

simplify8.0ms (0%)

prune2.0ms (0%)

localize7.0ms (0%)

series57.0ms (0.2%)

rewrite136.0ms (0.5%)

simplify67.0ms (0.2%)

prune226.0ms (0.8%)

localize18.0ms (0.1%)

series163.0ms (0.6%)

rewrite127.0ms (0.4%)

simplify89.0ms (0.3%)

prune349.0ms (1.2%)

localize22.0ms (0.1%)

series256.0ms (0.9%)

rewrite94.0ms (0.3%)

simplify80.0ms (0.3%)

prune349.0ms (1.2%)

localize22.0ms (0.1%)

series18.8s (64.6%)

rewrite84.0ms (0.3%)

simplify73.0ms (0.3%)

prune277.0ms (1%)

regimes993.0ms (3.4%)

simplify4.0ms (0%)

end267.0ms (0.9%)

Profiling