Details

analyze3.5s (17.1%)

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)

sample7.2s (35.8%)

Results

4.5s	3561×	body	1024	valid
1.1s	1445×	body	512	valid
705.0ms	2419×	body	128	valid
503.0ms	202×	body	2048	valid
329.0ms	629×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify13.0ms (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`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
2	16	14
3	20	14
4	21	14
5	21	14

prune6.0ms (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

14.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.1b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))

Compiler

Compiled 45 to 28 computations (37.8% saved)

localize15.0ms (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)))
✓	3.9b	(cos.f64 (+.f64 a b))

series172.0ms (0.8%)

Counts

3 → 52

Calls

3 calls:

106.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
56.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
9.0ms	(cos.f64 (+.f64 a b))

rewrite135.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

692×	`prod-diff_binary64`
214×	`fma-def_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
125×	`egg-rr`

Counts

3 → 125

Calls

3 calls:

128.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
128.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
128.0ms	(cos.f64 (+.f64 a b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	200	31
2	2736	31
3	4800	31
4	5016	31
0	0	0
1	0	0

simplify84.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-def_binary64`
622×	`associate-l_binary64`
444×	`associate-/r*_binary64`
196×	`associate-/r/_binary64`
178×	`associate-*l/_binary64`

Counts

177 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	1422
1	443	1420
2	1630	1358
3	5064	1358

prune514.0ms (2.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	153	16	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	16	170

Error

0.1b

Counts

170 → 16

Alt Table

Status	Error	Program
	31.7b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.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))))))))
	14.3b	(*.f64 r (/.f64 (sin.f64 b) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (+.f64 a b)))))))
	0.5b	(.f64 r (/.f64 (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)))))))
	0.5b	(.f64 r (/.f64 (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)))))))))
▶	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))))))
	24.0b	(.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 (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))))))
	0.5b	(.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)))))))))
	30.0b	(*.f64 r (/.f64 (sin.f64 b) (exp.f64 (log.f64 (cos.f64 (+.f64 a b))))))
	14.3b	(*.f64 r (/.f64 (sin.f64 b) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3))))
	33.7b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) r)) 2)
	14.1b	(/.f64 (neg.f64 (*.f64 (sin.f64 b) r)) (neg.f64 (cos.f64 (+.f64 a b))))
	14.2b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
	14.2b	(*.f64 r (log1p.f64 (expm1.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))))
	30.9b	(.f64 r (+.f64 (/.f64 (sin.f64 b) (cos.f64 b)) (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) a (fma.f64 1/2 (.f64 (/.f64 (sin.f64 b) (cos.f64 b)) (.f64 a a)) (/.f64 (.f64 (*.f64 a a) (pow.f64 (sin.f64 b) 3)) (pow.f64 (cos.f64 b) 3))))))
	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) (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))))))

Compiler

Compiled 5437 to 1874 computations (65.5% saved)

localize36.0ms (0.2%)

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 (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)))))
✓	52.4b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series502.0ms (2.5%)

Counts

4 → 108

Calls

4 calls:

279.0ms	(.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))))))
154.0ms	(/.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)))))
49.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))
19.0ms	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))

rewrite146.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

288×	`expm1-udef_binary64`
288×	`log1p-udef_binary64`
248×	`fma-neg_binary64`
179×	`add-sqr-sqrt_binary64`
165×	`log1p-expm1-u_binary64`

Counts

4 → 108

Calls

4 calls:

141.0ms	(.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))))))
141.0ms	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))
141.0ms	(/.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)))))
141.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	115
1	355	90
2	4040	90
3	5083	90
0	0	0
1	0	0

simplify133.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

743×	`fma-def_binary64`
675×	`associate-l_binary64`
444×	`associate-/r*_binary64`
196×	`associate-/r/_binary64`
178×	`associate-*l/_binary64`

Counts

216 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	2338
1	496	2328
2	1766	2244
3	5498	2244

prune1.1s (5.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	2	13	15
Picked	0	1	1
Done	0	0	0
Total	200	17	217

Error

0.0b

Counts

217 → 17

Alt Table

Status	Error	Program
	31.7b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.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))))))))
	14.3b	(*.f64 r (/.f64 (sin.f64 b) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (+.f64 a b)))))))
	0.5b	(.f64 r (/.f64 (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)))))))
	0.5b	(.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) (pow.f64 (cbrt.f64 (*.f64 (sin.f64 b) (sin.f64 a))) 3)))))
	0.5b	(.f64 r (/.f64 (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)))))))))
✓	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 (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))))))
	24.0b	(.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 (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))))))
	14.3b	(*.f64 r (/.f64 (sin.f64 b) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3))))
	33.7b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) r)) 2)
▶	0.3b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	14.2b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
	14.2b	(*.f64 r (log1p.f64 (expm1.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))))
	30.9b	(.f64 r (+.f64 (/.f64 (sin.f64 b) (cos.f64 b)) (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) a (fma.f64 1/2 (.f64 (/.f64 (sin.f64 b) (cos.f64 b)) (.f64 a a)) (/.f64 (.f64 (*.f64 a a) (pow.f64 (sin.f64 b) 3)) (pow.f64 (cos.f64 b) 3))))))
	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))))))))
	30.0b	(*.f64 r (/.f64 (sin.f64 b) (exp.f64 (log.f64 (cos.f64 (+.f64 a b))))))
	0.9b	(.f64 r (/.f64 (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))))))

Compiler

Compiled 8100 to 3311 computations (59.1% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series376.0ms (1.9%)

Counts

4 → 52

Calls

4 calls:

244.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
82.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
32.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
17.0ms	(*.f64 (sin.f64 b) r)

rewrite152.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

317×	`fma-neg_binary64`
277×	`expm1-udef_binary64`
277×	`log1p-udef_binary64`
155×	`egg-rr`
154×	`add-sqr-sqrt_binary64`

Counts

4 → 155

Calls

4 calls:

145.0ms	(*.f64 (sin.f64 b) r)
145.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
145.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
145.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	58
1	293	34
2	4064	34
3	5221	34
0	0	0
1	0	0

simplify89.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
682×	`fma-def_binary64`
663×	`associate-/l*_binary64`
311×	`cancel-sign-sub-inv_binary64`
154×	`fma-neg_binary64`

Counts

207 → 212

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	152	1361
1	469	1343
2	1620	1265
3	5256	1265

prune859.0ms (4.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	202	10	212
Fresh	8	7	15
Picked	1	0	1
Done	1	0	1
Total	212	17	229

Error

0.0b

Counts

229 → 17

Alt Table

Status	Error	Program
	0.5b	(.f64 r (/.f64 (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)))))))
	0.5b	(.f64 r (/.f64 (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)))))))))
	14.5b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (sqrt.f64 (cos.f64 a)) (.f64 (sqrt.f64 (cos.f64 a)) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
	13.0b	(.f64 (/.f64 (.f64 (sin.f64 b) r) (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))) (+.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (*.f64 (sin.f64 b) (sin.f64 a)) (cos.f64 (-.f64 b a)))))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a)))))
	31.0b	(/.f64 (pow.f64 (sqrt.f64 (.f64 (sin.f64 b) r)) 2) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.7b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 a)) 2) (.f64 (cbrt.f64 (cos.f64 a)) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
	30.9b	(.f64 r (+.f64 (/.f64 (sin.f64 b) (cos.f64 b)) (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) a (fma.f64 1/2 (.f64 (/.f64 (sin.f64 b) (cos.f64 b)) (.f64 a a)) (/.f64 (.f64 (*.f64 a a) (pow.f64 (sin.f64 b) 3)) (pow.f64 (cos.f64 b) 3))))))
	31.7b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.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))))))))
	14.2b	(.f64 (sin.f64 b) (.f64 r (/.f64 1 (cos.f64 (+.f64 b a)))))
	0.7b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 b)) 2) (.f64 (cbrt.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 (-.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 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))))))
	30.0b	(*.f64 r (/.f64 (sin.f64 b) (exp.f64 (log.f64 (cos.f64 (+.f64 a b))))))
	14.3b	(/.f64 (*.f64 (sin.f64 b) r) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 b a)) 3)))
	14.3b	(/.f64 (*.f64 (sin.f64 b) r) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (+.f64 b a))))))

Compiler

Compiled 5995 to 1857 computations (69% saved)

localize42.0ms (0.2%)

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 (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)))))
✓	5.3b	(log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a)))
	52.4b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series2.3s (11.1%)

Counts

2 → 48

Calls

2 calls:

1.4s

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

861.0ms

(/.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)))))

rewrite77.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

440×	`fma-def_binary64`
277×	`expm1-udef_binary64`
277×	`log1p-udef_binary64`
252×	`fma-neg_binary64`
178×	`add-sqr-sqrt_binary64`

Counts

2 → 84

Calls

2 calls:

75.0ms

(/.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)))))

75.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	51
1	353	44
2	3860	42
3	5293	42
0	0	0
1	0	0

simplify42.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

600×	`times-frac_binary64`
435×	`associate-/l*_binary64`
403×	`associate-r_binary64`
394×	`fma-def_binary64`
357×	`associate-l_binary64`

Counts

132 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1103
1	324	1095
2	1066	1047
3	4994	1047

prune373.0ms (1.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	183	17	200

Error

0.0b

Counts

200 → 17

Alt Table

Status	Error	Program
	14.5b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (sqrt.f64 (cos.f64 a)) (.f64 (sqrt.f64 (cos.f64 a)) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
	13.0b	(.f64 (/.f64 (.f64 (sin.f64 b) r) (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))) (+.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (*.f64 (sin.f64 b) (sin.f64 a)) (cos.f64 (-.f64 b a)))))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a)))))
	31.0b	(/.f64 (pow.f64 (sqrt.f64 (.f64 (sin.f64 b) r)) 2) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.7b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 a)) 2) (.f64 (cbrt.f64 (cos.f64 a)) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
	30.9b	(.f64 r (+.f64 (/.f64 (sin.f64 b) (cos.f64 b)) (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) a (fma.f64 1/2 (.f64 (/.f64 (sin.f64 b) (cos.f64 b)) (.f64 a a)) (/.f64 (.f64 (*.f64 a a) (pow.f64 (sin.f64 b) 3)) (pow.f64 (cos.f64 b) 3))))))
	0.5b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (.f64 (sin.f64 a) (pow.f64 (cbrt.f64 (sin.f64 b)) 2)) (cbrt.f64 (sin.f64 b))))) (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 (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))))))
	31.7b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.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))))))))
	0.5b	(.f64 r (/.f64 (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)))))))))
	14.2b	(.f64 (sin.f64 b) (.f64 r (/.f64 1 (cos.f64 (+.f64 b a)))))
	0.7b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 b)) 2) (.f64 (cbrt.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 (-.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))))))))
	30.0b	(*.f64 r (/.f64 (sin.f64 b) (exp.f64 (log.f64 (cos.f64 (+.f64 a b))))))
	14.3b	(/.f64 (*.f64 (sin.f64 b) r) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 b a)) 3)))
	14.3b	(/.f64 (*.f64 (sin.f64 b) r) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (+.f64 b a))))))

Compiler

Compiled 7216 to 2398 computations (66.8% saved)

regimes2.1s (10.5%)

Accuracy

Total 0.3b remaining (81.8%)

Threshold costs 0.3b (81.8%)

Counts

341 → 1

Compiler

Compiled 46229 to 27429 computations (40.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-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	21	50
1	31	50
2	35	50
3	37	50
4	36	50

end298.0ms (1.5%)

Compiler: Compiled 634 to 320 computations (49.5% saved)

Details

analyze3.5s (17.1%)

sample7.2s (35.8%)

simplify13.0ms (0.1%)

prune6.0ms (0%)

localize15.0ms (0.1%)

series172.0ms (0.8%)

rewrite135.0ms (0.7%)

simplify84.0ms (0.4%)

prune514.0ms (2.5%)

localize36.0ms (0.2%)

series502.0ms (2.5%)

rewrite146.0ms (0.7%)

simplify133.0ms (0.7%)

prune1.1s (5.3%)

localize25.0ms (0.1%)

series376.0ms (1.9%)

rewrite152.0ms (0.7%)

simplify89.0ms (0.4%)

prune859.0ms (4.2%)

localize42.0ms (0.2%)

series2.3s (11.1%)

rewrite77.0ms (0.4%)

simplify42.0ms (0.2%)

prune373.0ms (1.8%)

regimes2.1s (10.5%)

simplify3.0ms (0%)

end298.0ms (1.5%)

Profiling