Details

analyze1.6s (7.3%)

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 (18.2%)

Results

2.4s	3543×	body	1024	valid
595.0ms	1404×	body	512	valid
410.0ms	2482×	body	128	valid
315.0ms	231×	body	2048	valid
180.0ms	596×	body	256	valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess31.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

12×	`*-commutative_binary64`
8×	`associate-/l*_binary64`
4×	`associate-*r/_binary64`
4×	`associate-*l/_binary64`
4×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	56
1	39	56
2	55	56
3	69	56
4	73	56
0	3	3

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 12 to 8 computations (33.3% 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`

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
	15.4b	(/.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)

localize8.0ms (0%)

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)))
✓	2.7b	(cos.f64 (+.f64 a b))

series76.0ms (0.3%)

Counts

3 → 52

Calls

21 calls:

6.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))	r	0
5.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))	a	-inf
5.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))	a	inf
5.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))	r	-inf
5.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))	b	-inf

rewrite60.0ms (0.3%)

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

simplify39.0ms (0.2%)

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

prune217.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	156	12	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	158	12	170

Error

0.1b

Counts

170 → 12

Alt Table

Status	Error	Program
	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))))))))
	0.9b	(.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 (.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)))))))))
	15.6b	(*.f64 r (/.f64 (sin.f64 b) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 3)))
	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)))))))
	15.3b	(/.f64 (*.f64 (sin.f64 b) r) (cos.f64 (+.f64 a b)))
▶	0.3b	(.f64 r (/.f64 (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))))))
	0.4b	(.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)))))))))
	15.4b	(*.f64 r (/.f64 (sin.f64 b) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (+.f64 a b)))) 1)))
	30.9b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (sqrt.f64 (cos.f64 (+.f64 a b)))) (sqrt.f64 (cos.f64 (+.f64 a b))))
	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))))
	30.7b	(.f64 r (/.f64 (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))))))))
	23.2b	(.f64 r (/.f64 (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 5195 to 1734 computations (66.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 r (/.f64 (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))))))
✓	0.2b	(/.f64 (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)))))
✓	0.2b	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))
✓	52.5b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series249.0ms (1.1%)

Counts

4 → 108

Calls

27 calls:

21.0ms	(.f64 r (/.f64 (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))))))	r	inf
19.0ms	(.f64 r (/.f64 (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))))))	a	-inf
18.0ms	(.f64 r (/.f64 (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))))))	r	0
18.0ms	(.f64 r (/.f64 (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))))))	r	-inf
18.0ms	(/.f64 (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)))))	b	-inf

rewrite77.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

288×	`log1p-udef_binary64`
179×	`add-sqr-sqrt_binary64`
165×	`add-cbrt-cube_binary64`
165×	`log1p-expm1-u_binary64`
165×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	115
1	375	90
2	4798	90

Stop Event

1×	node limit

Counts

4 → 107

simplify55.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

743×	`fma-def_binary64`
676×	`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	175	2338
1	532	2328
2	1877	2244

Stop Event

1×	node limit

Counts

215 → 161

prune338.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	194	6	200
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	199	13	212

Error

0.1b

Counts

212 → 13

Alt Table

Status	Error	Program
	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))))))))
	0.9b	(.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 (.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)))))))))
	0.3b	(.f64 r (/.f64 (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))))))
	15.4b	(*.f64 r (/.f64 (sin.f64 b) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (+.f64 a b)))) 1)))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	15.6b	(*.f64 r (/.f64 (sin.f64 b) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 3)))
	15.4b	(.f64 r (.f64 (sin.f64 b) (/.f64 1 (+.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) 0) (fma.f64 (cos.f64 a) (cos.f64 b) (*.f64 (sin.f64 b) (sin.f64 a)))))))
▶	0.3b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (expm1.f64 (log1p.f64 (.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))))))
	0.3b	(.f64 r (/.f64 (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))))))
	30.9b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (sqrt.f64 (cos.f64 (+.f64 a b)))) (sqrt.f64 (cos.f64 (+.f64 a b))))
	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))))
	30.7b	(.f64 r (/.f64 (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))))))))
	0.3b	(.f64 r (/.f64 (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 (exp.f64 (log1p.f64 (*.f64 (sin.f64 b) (sin.f64 a)))) 1)))))

Compiler

Compiled 7895 to 3196 computations (59.5% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (expm1.f64 (log1p.f64 (.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)))))
	0.2b	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))
✓	0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
	52.5b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series82.0ms (0.4%)

Counts

2 → 40

Calls

12 calls:

17.0ms	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (expm1.f64 (log1p.f64 (.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)))))	a	inf
17.0ms	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (expm1.f64 (log1p.f64 (.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)))))	b	inf
16.0ms	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (expm1.f64 (log1p.f64 (.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)))))	a	-inf
16.0ms	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (expm1.f64 (log1p.f64 (.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)))))	b	-inf
4.0ms	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (expm1.f64 (log1p.f64 (.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)))))	a	0

rewrite61.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

270×	`log1p-udef_binary64`
173×	`add-sqr-sqrt_binary64`
163×	`expm1-log1p-u_binary64`
162×	`log1p-expm1-u_binary64`
160×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	51
1	383	34
2	4679	34

Stop Event

1×	node limit

Counts

2 → 68

simplify32.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

600×	`times-frac_binary64`
435×	`associate-/l*_binary64`
397×	`associate-r_binary64`
392×	`fma-def_binary64`
356×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1039
1	336	1031
2	1130	983

Stop Event

1×	node limit

Counts

108 → 100

prune321.0ms (1.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	167	13	180

Error

0.1b

Counts

180 → 13

Alt Table

Status	Error	Program
	16.3b	(.f64 r (.f64 (sin.f64 b) (/.f64 1 (+.f64 (cos.f64 (-.f64 b a)) (*.f64 (sin.f64 a) (+.f64 (sin.f64 b) (sin.f64 b)))))))
	0.9b	(.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 (.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)))))))))
	0.3b	(.f64 r (/.f64 (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))))))
	15.4b	(*.f64 r (/.f64 (sin.f64 b) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (+.f64 a b)))) 1)))
▶	0.3b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (expm1.f64 (log1p.f64 (.f64 (sin.f64 b) (sin.f64 a)))))) (fma.f64 (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) 1) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a)))))))
	30.7b	(.f64 r (/.f64 (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 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	15.6b	(*.f64 r (/.f64 (sin.f64 b) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 3)))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 (.f64 (+.f64 (.f64 (sin.f64 b) (sin.f64 a)) 1) (+.f64 (.f64 (sin.f64 b) (sin.f64 a)) 1)) 1) (+.f64 (+.f64 (.f64 (sin.f64 b) (sin.f64 a)) 1) 1)))))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))))))
✓	0.3b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (expm1.f64 (log1p.f64 (.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))))))
	0.3b	(.f64 r (/.f64 (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))))))
	30.9b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (sqrt.f64 (cos.f64 (+.f64 a b)))) (sqrt.f64 (cos.f64 (+.f64 a b))))
	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))))

Compiler

Compiled 6821 to 2481 computations (63.6% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (expm1.f64 (log1p.f64 (.f64 (sin.f64 b) (sin.f64 a)))))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))))
	0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
✓	3.6b	(log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a)))
✓	18.8b	(fma.f64 (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) 1) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))

series12.6s (57.9%)

Counts

3 → 72

Calls

18 calls:

5.0s	(fma.f64 (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) 1) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))	a	0
4.4s	(fma.f64 (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) 1) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))	b	0
602.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) 1) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))	b	inf
555.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) 1) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))	a	inf
550.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) 1) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a))))	a	-inf

rewrite38.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

190×	`add-sqr-sqrt_binary64`
179×	`expm1-log1p-u_binary64`
178×	`log1p-expm1-u_binary64`
175×	`add-cbrt-cube_binary64`
175×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	69
1	404	47

Stop Event

1×	node limit

Counts

3 → 117

simplify33.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

600×	`times-frac_binary64`
435×	`associate-/l*_binary64`
401×	`associate-r_binary64`
397×	`fma-def_binary64`
354×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	113	1127
1	342	1119
2	1146	1071

Stop Event

1×	node limit

Counts

189 → 150

prune388.0ms (1.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	198	13	211

Error

0.1b

Counts

211 → 13

Alt Table

Status	Error	Program
	16.3b	(.f64 r (.f64 (sin.f64 b) (/.f64 1 (+.f64 (cos.f64 (-.f64 b a)) (*.f64 (sin.f64 a) (+.f64 (sin.f64 b) (sin.f64 b)))))))
	0.9b	(.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 (.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)))))))))
	0.3b	(.f64 r (/.f64 (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))))))
	15.4b	(*.f64 r (/.f64 (sin.f64 b) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (+.f64 a b)))) 1)))
✓	0.3b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (expm1.f64 (log1p.f64 (.f64 (sin.f64 b) (sin.f64 a)))))) (fma.f64 (neg.f64 (sin.f64 b)) (*.f64 (sin.f64 a) 1) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a)))))))
	30.7b	(.f64 r (/.f64 (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 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	15.6b	(*.f64 r (/.f64 (sin.f64 b) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 3)))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 (.f64 (+.f64 (.f64 (sin.f64 b) (sin.f64 a)) 1) (+.f64 (.f64 (sin.f64 b) (sin.f64 a)) 1)) 1) (+.f64 (+.f64 (.f64 (sin.f64 b) (sin.f64 a)) 1) 1)))))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))))))
✓	0.3b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (expm1.f64 (log1p.f64 (.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))))))
	0.3b	(.f64 r (/.f64 (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))))))
	30.9b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (sqrt.f64 (cos.f64 (+.f64 a b)))) (sqrt.f64 (cos.f64 (+.f64 a b))))
	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))))

Compiler

Compiled 7708 to 2397 computations (68.9% saved)

regimes1.2s (5.4%)

Accuracy

Total 0.2b remaining (67.6%)

Threshold costs 0.2b (67.6%)

Counts

193 → 1

Compiler

Compiled 27685 to 16293 computations (41.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	50
1	32	50
2	36	50
3	38	50

Stop Event

1×

saturated

end243.0ms (1.1%)

Stop Event

1×

fuel

Compiler

Compiled 526 to 268 computations (49% saved)

Details

analyze1.6s (7.3%)

sample4.0s (18.2%)

preprocess31.0ms (0.1%)

simplify6.0ms (0%)

prune3.0ms (0%)

localize8.0ms (0%)

series76.0ms (0.3%)

rewrite60.0ms (0.3%)

simplify39.0ms (0.2%)

prune217.0ms (1%)

localize19.0ms (0.1%)

series249.0ms (1.1%)

rewrite77.0ms (0.4%)

simplify55.0ms (0.3%)

prune338.0ms (1.6%)

localize22.0ms (0.1%)

series82.0ms (0.4%)

rewrite61.0ms (0.3%)

simplify32.0ms (0.1%)

prune321.0ms (1.5%)

localize32.0ms (0.1%)

series12.6s (57.9%)

rewrite38.0ms (0.2%)

simplify33.0ms (0.2%)

prune388.0ms (1.8%)

regimes1.2s (5.4%)

simplify3.0ms (0%)

end243.0ms (1.1%)

Profiling