Details

analyze1.5s (13.7%)

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)

sample4.1s (38.4%)

Results

2.6s	3600×	body	1024	valid
599.0ms	1458×	body	512	valid
417.0ms	2388×	body	128	valid
297.0ms	207×	body	2048	valid
175.0ms	603×	body	256	valid
1.0ms	1×	body	1024	invalid

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`
2×	`associate-/r/_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
2	17	14
3	20	14
4	21	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

16.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	16.9b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))))
	17.0b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))

Compiler

Compiled 69 to 44 computations (36.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 b)
✓	0.1b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))))
✓	0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 b a)))
✓	4.2b	(cos.f64 (+.f64 b a))

series105.0ms (1%)

Counts

4 → 88

Calls

4 calls:

58.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))))
42.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 b a)))
4.0ms	(cos.f64 (+.f64 b a))
1.0ms	(sin.f64 b)

rewrite61.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

583×	`prod-diff_binary64`
214×	`fma-def_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
138×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	34
1	200	34
2	2862	34

Stop Event

1×	node limit

Counts

4 → 138

Calls

4 calls:

58.0ms	(sin.f64 b)
58.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))))
58.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 b a)))
58.0ms	(cos.f64 (+.f64 b a))

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

751×	`fma-def_binary64`
645×	`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	170	1746
1	515	1744
2	1840	1678

Stop Event

1×	node limit

Counts

226 → 192

prune286.0ms (2.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	176	16	192
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	177	17	194

Error

0.1b

Counts

194 → 17

Alt Table

Status	Error	Program
	0.4b	(.f64 r (/.f64 (sin.f64 b) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 b) (cos.f64 a)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)) (fma.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (cos.f64 b) (cos.f64 a)) (fma.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))))))))
	31.6b	(fma.f64 1/2 (.f64 (/.f64 (sin.f64 b) (cos.f64 b)) (.f64 (.f64 a a) r)) (fma.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) (.f64 a r) (/.f64 (pow.f64 (sin.f64 b) 3) (/.f64 (pow.f64 (cos.f64 b) 3) (.f64 (.f64 a a) r))))))
	24.0b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (sqrt.f64 (.f64 (cos.f64 b) (cos.f64 a))) (sqrt.f64 (.f64 (cos.f64 b) (cos.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))))
	26.2b	(/.f64 (sin.f64 b) (/.f64 (cos.f64 b) r))
	0.9b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a))) (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a)))) (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))))
▶	0.3b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))))
	0.3b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))
	31.9b	(+.f64 (/.f64 (.f64 b r) (cos.f64 a)) (+.f64 (/.f64 (.f64 (sin.f64 a) (.f64 r (pow.f64 b 2))) (pow.f64 (cos.f64 a) 2)) (+.f64 (.f64 2/3 (/.f64 (.f64 (sin.f64 a) (.f64 (pow.f64 b 4) r)) (pow.f64 (cos.f64 a) 2))) (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 a) 3) (.f64 (pow.f64 b 4) r)) (pow.f64 (cos.f64 a) 4)) (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 a) 2) (.f64 (pow.f64 b 3) r)) (pow.f64 (cos.f64 a) 3)) (.f64 1/3 (/.f64 (.f64 (pow.f64 b 3) r) (cos.f64 a))))))))
	0.9b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a))) (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a)))) (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a))) (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)))))))))
	39.8b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))) r) 3))
	17.0b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
	0.5b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (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))))))
	38.3b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))) r)) 2)
	39.3b	(*.f64 r (pow.f64 (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a)))) 2))
	17.1b	(/.f64 1 (/.f64 (cos.f64 (+.f64 b a)) (*.f64 (sin.f64 b) r)))
	0.5b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (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)))))))))
	32.4b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 b)) (sin.f64 a)) (sqrt.f64 (sin.f64 b))))) (fma.f64 (neg.f64 (.f64 (sqrt.f64 (sin.f64 b)) (sin.f64 a))) (sqrt.f64 (sin.f64 b)) (.f64 (.f64 (sqrt.f64 (sin.f64 b)) (sin.f64 a)) (sqrt.f64 (sin.f64 b)))))))

Compiler

Compiled 5743 to 2004 computations (65.1% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series198.0ms (1.9%)

Counts

4 → 100

Calls

4 calls:

110.0ms	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))))
64.0ms	(/.f64 (sin.f64 b) (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
14.0ms	(fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))
9.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

rewrite139.0ms (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	3771	39

Stop Event

1×	node limit

Counts

4 → 441

Calls

4 calls:

123.0ms	(fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))
123.0ms	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))))
123.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
123.0ms	(/.f64 (sin.f64 b) (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

840×	`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 → 509

prune932.0ms (8.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	500	9	509
Fresh	10	6	16
Picked	1	0	1
Done	0	0	0
Total	511	15	526

Error

0.0b

Counts

526 → 15

Alt Table

Status	Error	Program
	0.4b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (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))))))))
	28.2b	(fma.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r (*.f64 (/.f64 a (/.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (sin.f64 b) 2))) r))
	0.6b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (.f64 (cos.f64 b) (cbrt.f64 (pow.f64 (cos.f64 a) 2))) (cbrt.f64 (cos.f64 a)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b))) (pow.f64 (cbrt.f64 (sin.f64 a)) 2) (.f64 (*.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2))))))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 b) (cos.f64 a)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)) (fma.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (cos.f64 b) (cos.f64 a)) (fma.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))))))))
	0.9b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a))) (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a)))) (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (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)))))))
	17.0b	(*.f64 r (/.f64 (sin.f64 b) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 b a))))))
	38.3b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))) r)) 2)
	39.3b	(*.f64 r (pow.f64 (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a)))) 2))
▶	0.3b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.4b	(/.f64 (sin.f64 b) (/.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) r))
	0.7b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 b)) 2) (.f64 (cbrt.f64 (cos.f64 b)) (cos.f64 a)) (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 (pow.f64 (cbrt.f64 (cos.f64 b)) 2) (.f64 (cbrt.f64 (cos.f64 b)) (cos.f64 a)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b))) (pow.f64 (cbrt.f64 (sin.f64 a)) 2) (.f64 (*.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2))))))
	39.8b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))) r) 3))
	32.4b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 b) (cos.f64 a) (neg.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 b)) (sin.f64 a)) (sqrt.f64 (sin.f64 b))))) (fma.f64 (neg.f64 (.f64 (sqrt.f64 (sin.f64 b)) (sin.f64 a))) (sqrt.f64 (sin.f64 b)) (.f64 (.f64 (sqrt.f64 (sin.f64 b)) (sin.f64 a)) (sqrt.f64 (sin.f64 b)))))))

Compiler

Compiled 20128 to 5109 computations (74.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sin.f64 b) r)
✓	0.2b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
	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))))

series128.0ms (1.2%)

Counts

3 → 36

Calls

3 calls:

105.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
15.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
7.0ms	(*.f64 (sin.f64 b) r)

rewrite63.0ms (0.6%)

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

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
666×	`associate-/l*_binary64`
537×	`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 → 155

prune326.0ms (3.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	193	6	199
Fresh	10	4	14
Picked	0	1	1
Done	0	0	0
Total	203	11	214

Error

0.0b

Counts

214 → 11

Alt Table

Status	Error	Program
	1.3b	(/.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 (fma.f64 (cos.f64 b) (cos.f64 a) (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))))))))
	28.2b	(fma.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r (*.f64 (/.f64 a (/.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (sin.f64 b) 2))) r))
	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)))))))
▶	0.3b	(.f64 (/.f64 r (fma.f64 (sin.f64 b) (neg.f64 (sin.f64 a)) (.f64 (cos.f64 a) (cos.f64 b)))) (sin.f64 b))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 b) (neg.f64 (sin.f64 a))) 3)) (+.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (-.f64 (.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))))))))
✓	0.3b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.6b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (.f64 (cos.f64 b) (cbrt.f64 (pow.f64 (cos.f64 a) 2))) (cbrt.f64 (cos.f64 a)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b))) (pow.f64 (cbrt.f64 (sin.f64 a)) 2) (.f64 (*.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2))))))
	0.9b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a))) (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a)))) (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a))) (neg.f64 (.f64 (sin.f64 b) (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)))))
	17.1b	(*.f64 (/.f64 (sin.f64 b) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 b a)) 2))) (/.f64 r (cbrt.f64 (cos.f64 (+.f64 b a)))))

Compiler

Compiled 5047 to 1646 computations (67.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series222.0ms (2.1%)

Counts

4 → 104

Calls

4 calls:

102.0ms	(.f64 (/.f64 r (fma.f64 (sin.f64 b) (neg.f64 (sin.f64 a)) (.f64 (cos.f64 a) (cos.f64 b)))) (sin.f64 b))
96.0ms	(/.f64 r (fma.f64 (sin.f64 b) (neg.f64 (sin.f64 a)) (*.f64 (cos.f64 a) (cos.f64 b))))
16.0ms	(fma.f64 (sin.f64 b) (neg.f64 (sin.f64 a)) (*.f64 (cos.f64 a) (cos.f64 b)))
8.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

rewrite54.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

669×	`prod-diff_binary64`
144×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`
131×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	73
1	272	37
2	3687	37

Stop Event

1×	node limit

Counts

4 → 101

Calls

4 calls:

52.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
52.0ms	(fma.f64 (sin.f64 b) (neg.f64 (sin.f64 a)) (*.f64 (cos.f64 a) (cos.f64 b)))
52.0ms	(/.f64 r (fma.f64 (sin.f64 b) (neg.f64 (sin.f64 a)) (*.f64 (cos.f64 a) (cos.f64 b))))
52.0ms	(.f64 (/.f64 r (fma.f64 (sin.f64 b) (neg.f64 (sin.f64 a)) (.f64 (cos.f64 a) (cos.f64 b)))) (sin.f64 b))

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

914×	`fma-def_binary64`
478×	`associate-/r*_binary64`
217×	`associate-/r/_binary64`
193×	`cancel-sign-sub-inv_binary64`
187×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	2839
1	599	2821
2	2130	2714

Stop Event

1×	node limit

Counts

205 → 163

prune223.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	164	10	174

Error

0.0b

Counts

174 → 10

Alt Table

Status	Error	Program
	1.3b	(/.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 (fma.f64 (cos.f64 b) (cos.f64 a) (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))))))))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 b) (neg.f64 (sin.f64 a))) 3)) (+.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (-.f64 (.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))))))))
✓	0.3b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.6b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (.f64 (cos.f64 b) (cbrt.f64 (pow.f64 (cos.f64 a) 2))) (cbrt.f64 (cos.f64 a)) (neg.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b))) (pow.f64 (cbrt.f64 (sin.f64 a)) 2) (.f64 (*.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)) (pow.f64 (cbrt.f64 (sin.f64 a)) 2))))))
	0.4b	(.f64 (/.f64 r (fma.f64 (sin.f64 b) (neg.f64 (sin.f64 a)) (log1p.f64 (expm1.f64 (.f64 (cos.f64 a) (cos.f64 b)))))) (sin.f64 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)))))))
	0.9b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a))) (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a)))) (cbrt.f64 (.f64 (cos.f64 b) (cos.f64 a))) (neg.f64 (.f64 (sin.f64 b) (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)))))
	17.1b	(*.f64 (/.f64 (sin.f64 b) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 b a)) 2))) (/.f64 r (cbrt.f64 (cos.f64 (+.f64 b a)))))

Compiler

Compiled 3721 to 1460 computations (60.8% saved)

regimes1.9s (17.7%)

Accuracy

Total 0.3b remaining (79.8%)

Threshold costs 0.3b (79.8%)

Counts

397 → 1

Compiler

Compiled 33956 to 20914 computations (38.4% 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	13	26
1	19	26
2	21	26
3	22	26

Stop Event

1×

saturated

end199.0ms (1.9%)

Compiler: Compiled 367 to 203 computations (44.7% saved)

Details

analyze1.5s (13.7%)

sample4.1s (38.4%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series105.0ms (1%)

rewrite61.0ms (0.6%)

simplify49.0ms (0.5%)

prune286.0ms (2.7%)

localize32.0ms (0.3%)

series198.0ms (1.9%)

rewrite139.0ms (1.3%)

simplify70.0ms (0.7%)

prune932.0ms (8.7%)

localize12.0ms (0.1%)

series128.0ms (1.2%)

rewrite63.0ms (0.6%)

simplify33.0ms (0.3%)

prune326.0ms (3.1%)

localize14.0ms (0.1%)

series222.0ms (2.1%)

rewrite54.0ms (0.5%)

simplify59.0ms (0.6%)

prune223.0ms (2.1%)

regimes1.9s (17.7%)

simplify2.0ms (0%)

end199.0ms (1.9%)

Profiling