Details

analyze1.5s (12.2%)

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)

sample4.4s (35.9%)

Results

2.7s	3586×	body	1024	valid
589.0ms	1362×	body	512	valid
527.0ms	2444×	body	128	valid
325.0ms	225×	body	2048	valid
191.0ms	639×	body	256	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify45.0ms (0.4%)

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

12.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.9b	(/.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)))
✓	3.2b	(cos.f64 (+.f64 a b))

series68.0ms (0.6%)

Counts

3 → 68

Calls

3 calls:

57.0ms	(/.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))

rewrite100.0ms (0.8%)

Algorithm

1×	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:

97.0ms	(*.f64 r (sin.f64 b))
97.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
97.0ms	(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

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

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

prune218.0ms (1.8%)

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

0.0b

Counts

168 → 16

Alt Table

Status	Error	Program
	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)))))))
	13.0b	(.f64 (sin.f64 b) (.f64 r (/.f64 1 (cos.f64 (+.f64 a b)))))
	31.6b	(/.f64 (*.f64 r (sin.f64 b)) (pow.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3) 1/3))
	13.1b	(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (exp.f64 (cos.f64 (+.f64 a b)))))
	12.9b	(/.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 b) (sin.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))) (cos.f64 (-.f64 a b))))
	42.1b	(/.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 (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)))))
	32.9b	(+.f64 (fma.f64 (/.f64 b (cos.f64 a)) r (/.f64 (.f64 (sin.f64 a) (.f64 b (.f64 b r))) (pow.f64 (cos.f64 a) 2))) (.f64 (/.f64 (*.f64 (pow.f64 b 3) r) (cos.f64 a)) (+.f64 1/3 (/.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (cos.f64 a) 2)))))
	13.0b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	29.4b	(/.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 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))))))
	13.0b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	13.4b	(/.f64 (*.f64 r (sin.f64 b)) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 3))
	26.7b	(/.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)))))
	40.7b	(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 (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 5058 to 1600 computations (68.4% 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)))))
✓	54.9b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series193.0ms (1.6%)

Counts

3 → 84

Calls

3 calls:

160.0ms

(/.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))

rewrite111.0ms (0.9%)

Algorithm

1×	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

3 → 96

Calls

3 calls:

109.0ms

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

109.0ms

(/.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)))))

108.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

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

simplify72.0ms (0.6%)

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

180 → 130

Iterations

Useful iterations: 3 (0.0ms)

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

prune1.0s (8.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	190	4	194
Fresh	2	13	15
Picked	0	1	1
Done	0	0	0
Total	192	18	210

Error

0.0b

Counts

210 → 18

Alt Table

Status	Error	Program
	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)))))))
	13.0b	(.f64 (sin.f64 b) (.f64 r (/.f64 1 (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 (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))))))))
	13.0b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	13.4b	(/.f64 (*.f64 r (sin.f64 b)) (pow.f64 (cbrt.f64 (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 (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)))))
	31.6b	(/.f64 (*.f64 r (sin.f64 b)) (pow.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3) 1/3))
▶	0.3b	(/.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)))))
	13.1b	(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (exp.f64 (cos.f64 (+.f64 a b)))))
	12.7b	(.f64 (/.f64 (.f64 (sin.f64 b) r) (-.f64 (pow.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a))) 2) (pow.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) 0) 2))) (-.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a))) (.f64 (.f64 (sin.f64 b) (sin.f64 a)) 0)))
	40.7b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b))) 3))
	12.9b	(/.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 b) (sin.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))) (cos.f64 (-.f64 a b))))
	42.1b	(/.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 (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)))))
	32.9b	(+.f64 (fma.f64 (/.f64 b (cos.f64 a)) r (/.f64 (.f64 (sin.f64 a) (.f64 b (.f64 b r))) (pow.f64 (cos.f64 a) 2))) (.f64 (/.f64 (*.f64 (pow.f64 b 3) r) (cos.f64 a)) (+.f64 1/3 (/.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (cos.f64 a) 2)))))
	13.0b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	0.4b	(/.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))))))
	26.7b	(/.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)))))

Compiler

Compiled 8175 to 3284 computations (59.8% saved)

localize23.0ms (0.2%)

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 (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)))))
✓	3.4b	(-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 b) (sin.f64 a)))) 1)
	54.9b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series1.3s (10.6%)

Counts

3 → 76

Calls

3 calls:

855.0ms

(/.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)))))

430.0ms

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

9.0ms

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

rewrite90.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

904×	`prod-diff_binary64`
209×	`add-sqr-sqrt_binary64`
197×	`expm1-log1p-u_binary64`
196×	`log1p-expm1-u_binary64`
192×	`add-log-exp_binary64`

Counts

3 → 144

Calls

3 calls:

87.0ms

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

87.0ms

(/.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)))))

87.0ms

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	62
1	410	55
2	4425	40
3	5760	40

simplify87.0ms (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

220 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1811
1	379	1793
2	1298	1709
3	4862	1695
4	4984	1695
5	4977	1695

prune362.0ms (3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	16	16
Picked	1	0	1
Done	0	1	1
Total	163	18	181

Error

0.0b

Counts

181 → 18

Alt Table

Status	Error	Program
	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)))))))
	13.0b	(.f64 (sin.f64 b) (.f64 r (/.f64 1 (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 (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))))))))
	13.0b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	13.4b	(/.f64 (*.f64 r (sin.f64 b)) (pow.f64 (cbrt.f64 (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 (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)))))
	31.6b	(/.f64 (*.f64 r (sin.f64 b)) (pow.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3) 1/3))
	13.1b	(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (exp.f64 (cos.f64 (+.f64 a b)))))
	12.7b	(.f64 (/.f64 (.f64 (sin.f64 b) r) (-.f64 (pow.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a))) 2) (pow.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) 0) 2))) (-.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a))) (.f64 (.f64 (sin.f64 b) (sin.f64 a)) 0)))
	40.7b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b))) 3))
	12.9b	(/.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 b) (sin.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))) (cos.f64 (-.f64 a b))))
	42.1b	(/.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 (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)))))
	32.9b	(+.f64 (fma.f64 (/.f64 b (cos.f64 a)) r (/.f64 (.f64 (sin.f64 a) (.f64 b (.f64 b r))) (pow.f64 (cos.f64 a) 2))) (.f64 (/.f64 (*.f64 (pow.f64 b 3) r) (cos.f64 a)) (+.f64 1/3 (/.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (cos.f64 a) 2)))))
	13.0b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	0.4b	(/.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))))))
▶	0.3b	(/.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))) 0))
	26.7b	(/.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)))))

Compiler

Compiled 6915 to 2684 computations (61.2% 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) (sin.f64 a))
✓	0.2b	(/.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))) 0))
	3.4b	(-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 b) (sin.f64 a)))) 1)

series838.0ms (6.8%)

Counts

1 → 36

Calls

1 calls:

838.0ms

(/.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))) 0))

rewrite102.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

422×	`fma-neg_binary64`
284×	`log1p-udef_binary64`
283×	`expm1-udef_binary64`
177×	`add-sqr-sqrt_binary64`
170×	`expm1-log1p-u_binary64`

Counts

1 → 46

Calls

1 calls:

101.0ms

(/.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))) 0))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	26
1	358	14
2	4122	14
3	4973	14
4	5308	14

simplify40.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
664×	`associate-/l*_binary64`
455×	`associate-r_binary64`
390×	`associate-l_binary64`
355×	`fma-def_binary64`

Counts

82 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1211
1	271	1209
2	962	1173
3	5441	1173

prune303.0ms (2.5%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	3	13	16
Picked	0	1	1
Done	0	1	1
Total	165	18	183

Error

0.0b

Counts

183 → 18

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 (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))))))))
	13.0b	(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
	26.7b	(/.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)))))
	13.1b	(.f64 (/.f64 (.f64 r (sin.f64 b)) (pow.f64 (cos.f64 (-.f64 b a)) 2)) (cos.f64 (-.f64 b a)))
	31.6b	(/.f64 (*.f64 r (sin.f64 b)) (pow.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3) 1/3))
	13.1b	(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (exp.f64 (cos.f64 (+.f64 a b)))))
	40.7b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b))) 3))
	13.0b	(*.f64 (/.f64 r (cos.f64 (-.f64 b a))) (sin.f64 b))
	12.9b	(/.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 b) (sin.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))) (cos.f64 (-.f64 a b))))
	42.1b	(/.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 (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)))))
	32.9b	(+.f64 (fma.f64 (/.f64 b (cos.f64 a)) r (/.f64 (.f64 (sin.f64 a) (.f64 b (.f64 b r))) (pow.f64 (cos.f64 a) 2))) (.f64 (/.f64 (*.f64 (pow.f64 b 3) r) (cos.f64 a)) (+.f64 1/3 (/.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (cos.f64 a) 2)))))
	13.0b	(pow.f64 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))) -1)
	0.3b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 a) 3) (pow.f64 (sin.f64 b) 3))))) 0))
	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)))))))
	0.4b	(/.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))))))
	13.4b	(/.f64 (*.f64 r (sin.f64 b)) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 3))
✓	0.3b	(/.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))) 0))

Compiler

Compiled 4703 to 1993 computations (57.6% saved)

regimes921.0ms (7.5%)

Accuracy

Total 0.2b remaining (74.4%)

Threshold costs 0.2b (74.4%)

Counts

187 → 1

Compiler

Compiled 20492 to 12308 computations (39.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-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	21	50
1	34	50
2	46	50
3	49	50
4	50	50
5	48	50

end368.0ms (3%)

Compiler: Compiled 583 to 324 computations (44.4% saved)

Details

analyze1.5s (12.2%)

sample4.4s (35.9%)

simplify45.0ms (0.4%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series68.0ms (0.6%)

rewrite100.0ms (0.8%)

simplify63.0ms (0.5%)

prune218.0ms (1.8%)

localize18.0ms (0.1%)

series193.0ms (1.6%)

rewrite111.0ms (0.9%)

simplify72.0ms (0.6%)

prune1.0s (8.3%)

localize23.0ms (0.2%)

series1.3s (10.6%)

rewrite90.0ms (0.7%)

simplify87.0ms (0.7%)

prune362.0ms (3%)

localize18.0ms (0.1%)

series838.0ms (6.8%)

rewrite102.0ms (0.8%)

simplify40.0ms (0.3%)

prune303.0ms (2.5%)

regimes921.0ms (7.5%)

simplify3.0ms (0%)

end368.0ms (3%)

Profiling