Details

analyze1.6s (13.9%)

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 (34.7%)

Results

2.4s	3599×	body	1024	valid
625.0ms	1425×	body	512	valid
385.0ms	2444×	body	128	valid
304.0ms	230×	body	2048	valid
171.0ms	558×	body	256	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
2	17	14
3	21	14
4	22	14

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

15.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	15.3b	(/.f64 r (/.f64 (cos.f64 (+.f64 b a)) (sin.f64 b)))
▶	15.3b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))

Compiler

Compiled 69 to 44 computations (36.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
✓	0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
✓	3.0b	(cos.f64 (+.f64 a b))

series65.0ms (0.6%)

Counts

3 → 52

Calls

3 calls:

39.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
22.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
3.0ms	(cos.f64 (+.f64 a b))

rewrite57.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

588×	`prod-diff_binary64`
214×	`fma-def_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
123×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	200	31
2	2864	31

Stop Event

1×	node limit

Counts

3 → 123

Calls

3 calls:

54.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
54.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
54.0ms	(cos.f64 (+.f64 a b))

simplify35.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
619×	`associate-l_binary64`
441×	`associate-/r*_binary64`
196×	`associate-/r/_binary64`
178×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	1422
1	469	1420
2	1708	1358

Stop Event

1×	node limit

Counts

175 → 168

prune244.0ms (2.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	153	15	168
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	154	16	170

Error

0.1b

Counts

170 → 16

Alt Table

Status	Error	Program
	15.4b	(*.f64 r (/.f64 (sin.f64 b) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3))))
	30.6b	(fma.f64 1/2 (.f64 (/.f64 (sin.f64 b) (cos.f64 b)) (.f64 a (.f64 a r))) (fma.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r (fma.f64 5/6 (.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 a 3) r)) (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) (.f64 a r) (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 3) (pow.f64 (cos.f64 b) 3)) (.f64 a (.f64 a r)) (.f64 (/.f64 (pow.f64 (sin.f64 b) 4) (pow.f64 (cos.f64 b) 4)) (.f64 (pow.f64 a 3) r)))))))
	29.8b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (sqrt.f64 (cos.f64 (+.f64 a b)))) (sqrt.f64 (cos.f64 (+.f64 a b))))
	21.8b	(.f64 r (/.f64 (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 (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)))))))
	30.4b	(fma.f64 (/.f64 b (cos.f64 a)) r (.f64 (.f64 (/.f64 (sin.f64 a) (/.f64 (pow.f64 (cos.f64 a) 2) b)) b) r))
	15.6b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (cbrt.f64 (cos.f64 (+.f64 a b))))
	0.8b	(.f64 r (/.f64 (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 (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)))))))
	15.3b	(/.f64 r (/.f64 (cos.f64 (+.f64 b a)) (sin.f64 b)))
	0.4b	(.f64 r (/.f64 (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)))) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a))))))
	38.5b	(*.f64 r (pow.f64 (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) 2))
	15.3b	(/.f64 (*.f64 (neg.f64 (sin.f64 b)) r) (neg.f64 (cos.f64 (+.f64 a b))))
	0.4b	(.f64 r (/.f64 (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 r (/.f64 (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))))))))
	0.5b	(.f64 r (/.f64 (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)))))))))
	39.5b	(.f64 r (.f64 (sqrt.f64 (sin.f64 b)) (*.f64 (sqrt.f64 (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a b))))))
▶	0.3b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))))

Compiler

Compiled 5439 to 1908 computations (64.9% saved)

localize14.0ms (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 b) (sin.f64 a))))
✓	0.2b	(.f64 r (/.f64 (sin.f64 b) (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 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))

series178.0ms (1.6%)

Counts

4 → 100

Calls

4 calls:

100.0ms	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))))
54.0ms	(/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
16.0ms	(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))
8.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

rewrite146.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

770×	`prod-diff_binary64`
441×	`egg-rr`
145×	`add-sqr-sqrt_binary64`
133×	`log1p-expm1-u_binary64`
133×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	75
1	275	39
2	3778	39

Stop Event

1×	node limit

Counts

4 → 441

Calls

4 calls:

129.0ms	(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))
129.0ms	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))))
129.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
129.0ms	(/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

841×	`fma-def_binary64`
438×	`associate-/r*_binary64`
236×	`cancel-sign-sub-inv_binary64`
196×	`associate-/r/_binary64`
178×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	187	2682
1	578	2672
2	2048	2586

Stop Event

1×	node limit

Counts

541 → 508

prune842.0ms (7.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	501	7	508
Fresh	6	9	15
Picked	1	0	1
Done	0	0	0
Total	508	16	524

Error

0.0b

Counts

524 → 16

Alt Table

Status	Error	Program
	29.8b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (sqrt.f64 (cos.f64 (+.f64 a b)))) (sqrt.f64 (cos.f64 (+.f64 a b))))
	0.5b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (.f64 (cos.f64 a) (cbrt.f64 (pow.f64 (cos.f64 b) 2))) (cbrt.f64 (cos.f64 b)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (cbrt.f64 (pow.f64 (sin.f64 b) 2))))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a))) (cbrt.f64 (pow.f64 (sin.f64 b) 2)) (.f64 (*.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (cbrt.f64 (pow.f64 (sin.f64 b) 2)))))))
	30.4b	(fma.f64 (/.f64 b (cos.f64 a)) r (.f64 (.f64 (/.f64 (sin.f64 a) (/.f64 (pow.f64 (cos.f64 a) 2) b)) b) r))
	14.7b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (.f64 (cos.f64 a) (sqrt.f64 (cos.f64 b))) (sqrt.f64 (cos.f64 b)) (neg.f64 (.f64 (cbrt.f64 (sin.f64 b)) (.f64 (sin.f64 a) (cbrt.f64 (pow.f64 (sin.f64 b) 2)))))) (fma.f64 (neg.f64 (cbrt.f64 (sin.f64 b))) (.f64 (sin.f64 a) (cbrt.f64 (pow.f64 (sin.f64 b) 2))) (.f64 (cbrt.f64 (sin.f64 b)) (*.f64 (sin.f64 a) (cbrt.f64 (pow.f64 (sin.f64 b) 2))))))))
	15.6b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (cbrt.f64 (cos.f64 (+.f64 a b))))
	0.6b	(.f64 r (/.f64 (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 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (cbrt.f64 (pow.f64 (sin.f64 b) 2))))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a))) (cbrt.f64 (pow.f64 (sin.f64 b) 2)) (.f64 (*.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (cbrt.f64 (pow.f64 (sin.f64 b) 2)))))))
	0.8b	(.f64 r (/.f64 (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 (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)))))))
	26.9b	(*.f64 r (cbrt.f64 (/.f64 (pow.f64 (sin.f64 b) 3) (pow.f64 (cos.f64 (-.f64 b a)) 3))))
	0.4b	(.f64 r (/.f64 (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)))) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a))))))
	15.3b	(/.f64 r (/.f64 (cos.f64 (+.f64 b a)) (sin.f64 b)))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a)))))))))
	15.4b	(*.f64 r (/.f64 (sin.f64 b) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3))))
	38.5b	(*.f64 r (pow.f64 (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) 2))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 b) (sin.f64 a)))) 1)))))
	0.4b	(.f64 r (/.f64 (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 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))

Compiler

Compiled 20090 to 5112 computations (74.6% 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 b) (sin.f64 a)))
✓	0.1b	(*.f64 (sin.f64 b) r)
	0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
✓	0.2b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))

series114.0ms (1%)

Counts

3 → 36

Calls

3 calls:

94.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
13.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
6.0ms	(*.f64 (sin.f64 b) r)

rewrite62.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

277×	`expm1-udef_binary64`
277×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
148×	`log1p-expm1-u_binary64`
148×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	50
1	297	26
2	4363	26

Stop Event

1×	node limit

Counts

3 → 113

Calls

3 calls:

60.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
60.0ms	(*.f64 (sin.f64 b) r)
60.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))

simplify31.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
666×	`associate-/l*_binary64`
529×	`fma-def_binary64`
310×	`associate-/r*_binary64`
154×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1093
1	420	1083
2	1463	1035

Stop Event

1×	node limit

Counts

149 → 154

prune374.0ms (3.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	187	11	198
Fresh	9	6	15
Picked	1	0	1
Done	0	0	0
Total	197	17	214

Error

0.0b

Counts

214 → 17

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (.f64 (sin.f64 b) (neg.f64 (sin.f64 a))) (.f64 (sin.f64 b) (neg.f64 (sin.f64 a))))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (neg.f64 (sin.f64 a))))))
	15.3b	(.f64 r (.f64 (sin.f64 b) (/.f64 1 (cos.f64 (+.f64 b a)))))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 b) (sin.f64 a)))) 1)))
	15.3b	(.f64 (sin.f64 b) (.f64 r (/.f64 1 (cos.f64 (+.f64 b a)))))
	38.5b	(*.f64 r (pow.f64 (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) 2))
	28.9b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (pow.f64 (sqrt.f64 (*.f64 (sin.f64 b) (sin.f64 a))) 2)))
	29.8b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (sqrt.f64 (cos.f64 (+.f64 a b)))) (sqrt.f64 (cos.f64 (+.f64 a b))))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))))
	30.4b	(fma.f64 (/.f64 b (cos.f64 a)) r (.f64 (.f64 (/.f64 (sin.f64 a) (/.f64 (pow.f64 (cos.f64 a) 2) b)) b) r))
	0.6b	(.f64 r (/.f64 (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 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (cbrt.f64 (pow.f64 (sin.f64 b) 2))))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a))) (cbrt.f64 (pow.f64 (sin.f64 b) 2)) (.f64 (*.f64 (cbrt.f64 (sin.f64 b)) (sin.f64 a)) (cbrt.f64 (pow.f64 (sin.f64 b) 2)))))))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))))
	0.8b	(.f64 r (/.f64 (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 (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 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (pow.f64 (cbrt.f64 (*.f64 (sin.f64 b) (sin.f64 a))) 3)))
▶	0.3b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (neg.f64 (sin.f64 a)))))
	15.3b	(*.f64 (/.f64 (sin.f64 b) 1) (/.f64 r (cos.f64 (+.f64 b a))))
	1.2b	(/.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 b) r)) 3) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.4b	(.f64 r (/.f64 (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)))) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (sin.f64 a))))))

Compiler

Compiled 5272 to 1799 computations (65.9% 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) (*.f64 (sin.f64 b) (neg.f64 (sin.f64 a))))
	0.1b	(*.f64 (sin.f64 b) r)
✓	0.2b	(*.f64 (sin.f64 b) (neg.f64 (sin.f64 a)))
✓	0.2b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (neg.f64 (sin.f64 a)))))

series123.0ms (1.1%)

Counts

3 → 84

Calls

3 calls:

98.0ms

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

14.0ms

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

10.0ms

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

rewrite85.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

333×	`prod-diff_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
202×	`egg-rr`
139×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	54
1	267	48
2	3587	48

Stop Event

1×	node limit

Counts

3 → 202

Calls

3 calls:

79.0ms

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

79.0ms

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

79.0ms

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

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
667×	`associate-/l*_binary64`
655×	`fma-def_binary64`
174×	`cancel-sign-sub-inv_binary64`
148×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	2011
1	475	2009
2	1575	1943

Stop Event

1×	node limit

Counts

286 → 255

prune610.0ms (5.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	272	6	278
Fresh	7	9	16
Picked	0	1	1
Done	0	0	0
Total	279	16	295

Error

0.0b

Counts

295 → 16

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (.f64 (sin.f64 b) (neg.f64 (sin.f64 a))) (.f64 (sin.f64 b) (neg.f64 (sin.f64 a))))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (neg.f64 (sin.f64 a))))))
	15.3b	(.f64 r (.f64 (sin.f64 b) (/.f64 1 (cos.f64 (+.f64 b a)))))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (-.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 b) (sin.f64 a)))) 1)))
	15.3b	(.f64 (sin.f64 b) (.f64 r (/.f64 1 (cos.f64 (+.f64 b a)))))
	38.5b	(*.f64 r (pow.f64 (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) 2))
	0.7b	(/.f64 (.f64 (sin.f64 b) r) (+.f64 (fma.f64 (.f64 (cos.f64 a) (pow.f64 (cbrt.f64 (cos.f64 b)) 2)) (cbrt.f64 (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))))))
	29.8b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (sqrt.f64 (cos.f64 (+.f64 a b)))) (sqrt.f64 (cos.f64 (+.f64 a b))))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))))
	14.7b	(/.f64 (.f64 (sin.f64 b) r) (+.f64 (fma.f64 (.f64 (cos.f64 a) (sqrt.f64 (cos.f64 b))) (sqrt.f64 (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)))))
	26.6b	(fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) (*.f64 r a) (/.f64 r (/.f64 (cos.f64 b) (sin.f64 b))))
	1.2b	(/.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 b) r)) 3) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (neg.f64 (sin.f64 a)))))
✓	0.3b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (cos.f64 a) (cos.f64 b) (.f64 (sin.f64 b) (neg.f64 (sin.f64 a)))))
	0.8b	(.f64 r (/.f64 (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 (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)))))))
	15.3b	(*.f64 (/.f64 (sin.f64 b) 1) (/.f64 r (cos.f64 (+.f64 b a))))
	0.6b	(/.f64 (.f64 (sin.f64 b) r) (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 a)) 2) (.f64 (cbrt.f64 (cos.f64 a)) (cos.f64 b)) (neg.f64 (.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))) (fma.f64 (sin.f64 a) (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))))
	0.3b	(/.f64 (.f64 (sin.f64 b) r) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))) (fma.f64 (sin.f64 a) (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))))

Compiler

Compiled 9683 to 2425 computations (75% saved)

regimes2.4s (21.3%)

Accuracy

Total 0.3b remaining (76%)

Threshold costs 0.3b (76%)

Counts

360 → 1

Compiler

Compiled 48778 to 27050 computations (44.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	30
1	21	30
2	23	30
3	24	30

Stop Event

1×

saturated

end268.0ms (2.3%)

Compiler: Compiled 526 to 289 computations (45.1% saved)

Details

analyze1.6s (13.9%)

sample4.0s (34.7%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series65.0ms (0.6%)

rewrite57.0ms (0.5%)

simplify35.0ms (0.3%)

prune244.0ms (2.1%)

localize14.0ms (0.1%)

series178.0ms (1.6%)

rewrite146.0ms (1.3%)

simplify68.0ms (0.6%)

prune842.0ms (7.4%)

localize12.0ms (0.1%)

series114.0ms (1%)

rewrite62.0ms (0.5%)

simplify31.0ms (0.3%)

prune374.0ms (3.3%)

localize12.0ms (0.1%)

series123.0ms (1.1%)

rewrite85.0ms (0.7%)

simplify79.0ms (0.7%)

prune610.0ms (5.3%)

regimes2.4s (21.3%)

simplify2.0ms (0%)

end268.0ms (2.3%)

Profiling