Details

analyze1.7s (16.5%)

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)

sample4.3s (40.8%)

Results

2.6s	3586×	body	1024	valid
567.0ms	1362×	body	512	valid
496.0ms	2444×	body	128	valid
372.0ms	225×	body	2048	valid
239.0ms	639×	body	256	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify9.0ms (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

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

12.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.9b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))

Compiler

Compiled 45 to 28 computations (37.8% saved)

localize8.0ms (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)))
✓	3.2b	(cos.f64 (+.f64 a b))

series70.0ms (0.7%)

Counts

3 → 52

Calls

3 calls:

41.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
24.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
4.0ms	(cos.f64 (+.f64 a b))

rewrite100.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Counts

3 → 128

Calls

3 calls:

96.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
96.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
96.0ms	(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

simplify47.0ms (0.5%)

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

180 → 172

Iterations

Useful iterations: 2 (0.0ms)

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

prune212.0ms (2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	157	15	172
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	158	15	173

Error

0.1b

Counts

173 → 15

Alt Table

Status	Error	Program
	31.7b	(/.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 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)) (fma.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b)) (fma.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))))))
	13.7b	(.f64 r (.f64 (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) 2)))
	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))))))
	31.6b	(*.f64 r (/.f64 (sin.f64 b) (pow.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3) 1/3)))
	0.4b	(.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)))))))
	26.7b	(.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))))))
	13.4b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (cbrt.f64 (cos.f64 (+.f64 a b))))
	13.0b	(/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 (sin.f64 b) r)))
	13.0b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
	32.9b	(+.f64 (fma.f64 (/.f64 b (cos.f64 a)) r (.f64 (/.f64 (.f64 b (.f64 b (sin.f64 a))) (pow.f64 (cos.f64 a) 2)) r)) (.f64 (*.f64 (/.f64 (pow.f64 b 3) (cos.f64 a)) r) (+.f64 1/3 (/.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (cos.f64 a) 2)))))
	18.2b	(*.f64 r (expm1.f64 (log1p.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))))
	12.9b	(/.f64 (*.f64 (sin.f64 b) r) (cos.f64 (+.f64 a b)))
	13.1b	(*.f64 r (/.f64 (sin.f64 b) (log.f64 (exp.f64 (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))))))

Compiler

Compiled 5084 to 1783 computations (64.9% saved)

localize18.0ms (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 (.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 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))))))
✓	54.9b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series238.0ms (2.3%)

Counts

4 → 108

Calls

4 calls:

135.0ms	(.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))))))
69.0ms	(/.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)))))
24.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))
10.0ms	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))

rewrite83.0ms (0.8%)

Algorithm

1×	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 → 111

Calls

4 calls:

80.0ms	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))
80.0ms	(/.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)))))
80.0ms	(.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))))))
80.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

Iterations

Useful iterations: 1 (0.0ms)

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

simplify64.0ms (0.6%)

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

219 → 161

Iterations

Useful iterations: 2 (0.0ms)

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

prune315.0ms (3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	198	2	200
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	201	14	215

Error

0.1b

Counts

215 → 14

Alt Table

Status	Error	Program
	31.7b	(/.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 (-.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))))))))
	18.2b	(*.f64 r (expm1.f64 (log1p.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))))
	0.3b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.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 (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))
	13.1b	(*.f64 r (/.f64 (sin.f64 b) (log.f64 (exp.f64 (cos.f64 (+.f64 a b))))))
	31.6b	(*.f64 r (/.f64 (sin.f64 b) (pow.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3) 1/3)))
	0.4b	(.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)))))))
	26.7b	(.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))))))
	13.4b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (cbrt.f64 (cos.f64 (+.f64 a b))))
	13.0b	(/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 (sin.f64 b) r)))
	13.0b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
	32.9b	(+.f64 (fma.f64 (/.f64 b (cos.f64 a)) r (.f64 (/.f64 (.f64 b (.f64 b (sin.f64 a))) (pow.f64 (cos.f64 a) 2)) r)) (.f64 (*.f64 (/.f64 (pow.f64 b 3) (cos.f64 a)) r) (+.f64 1/3 (/.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (cos.f64 a) 2)))))
	13.7b	(.f64 r (.f64 (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) 2)))

Compiler

Compiled 7742 to 3170 computations (59.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
✓	0.2b	(/.f64 (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) (log1p.f64 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a)))))))
✓	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) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))
✓	54.9b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (log1p.f64 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a)))))

series230.0ms (2.2%)

Counts

4 → 100

Calls

4 calls:

127.0ms	(.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) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))
69.0ms	(/.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) (log1p.f64 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a)))))))
25.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (log1p.f64 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a)))))
9.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

rewrite119.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

314×	`log1p-udef_binary64`
313×	`expm1-udef_binary64`
194×	`add-sqr-sqrt_binary64`
182×	`expm1-log1p-u_binary64`
181×	`log1p-expm1-u_binary64`

Counts

4 → 115

Calls

4 calls:

116.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
116.0ms	(/.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) (log1p.f64 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a)))))))
116.0ms	(.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) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))
115.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (log1p.f64 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a)))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	115
1	383	90
2	4445	90
3	4962	90
4	5296	90

simplify63.0ms (0.6%)

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

215 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	2274
1	496	2264
2	1766	2180
3	5498	2180

prune213.0ms (2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	165	14	179

Error

0.1b

Counts

179 → 14

Alt Table

Status	Error	Program
	31.7b	(/.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 (-.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))))))))
	18.2b	(*.f64 r (expm1.f64 (log1p.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))))
▶	0.3b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.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 (.f64 (sin.f64 b) (.f64 (sin.f64 a) 1)))) (fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))))
	13.1b	(*.f64 r (/.f64 (sin.f64 b) (log.f64 (exp.f64 (cos.f64 (+.f64 a b))))))
	31.6b	(*.f64 r (/.f64 (sin.f64 b) (pow.f64 (pow.f64 (cos.f64 (+.f64 a b)) 3) 1/3)))
	0.4b	(.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)))))))
	26.7b	(.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))))))
	13.4b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (cbrt.f64 (cos.f64 (+.f64 a b))))
	13.0b	(/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 (sin.f64 b) r)))
	13.0b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
	32.9b	(+.f64 (fma.f64 (/.f64 b (cos.f64 a)) r (.f64 (/.f64 (.f64 b (.f64 b (sin.f64 a))) (pow.f64 (cos.f64 a) 2)) r)) (.f64 (*.f64 (/.f64 (pow.f64 b 3) (cos.f64 a)) r) (+.f64 1/3 (/.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (cos.f64 a) 2)))))
	13.7b	(.f64 r (.f64 (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) 2)))

Compiler

Compiled 6440 to 2654 computations (58.8% saved)

localize13.0ms (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))))

series124.0ms (1.2%)

Counts

3 → 36

Calls

3 calls:

101.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
16.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
7.0ms	(*.f64 (sin.f64 b) r)

rewrite76.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

317×	`fma-neg_binary64`
277×	`expm1-udef_binary64`
277×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
148×	`log1p-expm1-u_binary64`

Counts

3 → 140

Calls

3 calls:

73.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
73.0ms	(*.f64 (sin.f64 b) r)
73.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	50
1	293	26
2	4064	26
3	5221	26

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

833×	`times-frac_binary64`
663×	`associate-/l*_binary64`
538×	`fma-def_binary64`
310×	`associate-/r*_binary64`
181×	`fma-neg_binary64`

Counts

176 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1093
1	394	1083
2	1368	1035
3	4952	1035
4	5013	1035

prune341.0ms (3.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	213	11	224
Fresh	6	6	12
Picked	1	0	1
Done	0	1	1
Total	220	18	238

Error

0.0b

Counts

238 → 18

Alt Table

Status	Error	Program
	16.5b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (sqrt.f64 (cos.f64 b)) (.f64 (sqrt.f64 (cos.f64 b)) (cos.f64 a)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
	11.6b	(/.f64 (.f64 (sin.f64 b) r) (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)) (/.f64 1 (+.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 2) (.f64 (*.f64 (sin.f64 b) (sin.f64 a)) (cos.f64 (-.f64 b a)))))))
✓	0.3b	(.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) (log1p.f64 (expm1.f64 (*.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 a) (sin.f64 b))))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
	0.6b	(/.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)))))
	0.3b	(/.f64 (.f64 (sin.f64 b) r) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.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 (.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)))))))
	27.1b	(/.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))))
	13.0b	(.f64 (sin.f64 b) (.f64 r (/.f64 1 (cos.f64 (+.f64 b a)))))
	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))))
	13.4b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (cbrt.f64 (cos.f64 (+.f64 a b))))
	13.0b	(/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 (sin.f64 b) r)))
	13.0b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
	18.2b	(*.f64 r (expm1.f64 (log1p.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))))
	13.7b	(.f64 r (.f64 (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) 2)))
	13.0b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 1 (/.f64 (cos.f64 (-.f64 b a)) (.f64 (cos.f64 (-.f64 b a)) (cos.f64 (+.f64 b a))))))
	0.3b	(/.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)))

Compiler

Compiled 5532 to 1612 computations (70.9% saved)

regimes1.6s (15.8%)

Accuracy

Total 0.3b remaining (81.6%)

Threshold costs 0.3b (81.6%)

Counts

219 → 1

Compiler

Compiled 27195 to 16686 computations (38.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`distribute-rgt-neg-in_binary64`
3×	`distribute-lft-neg-in_binary64`
3×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	34	50
2	46	50
3	49	50
4	50	50
5	48	50

end392.0ms (3.7%)

Compiler: Compiled 498 to 297 computations (40.4% saved)

Details

analyze1.7s (16.5%)

sample4.3s (40.8%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series70.0ms (0.7%)

rewrite100.0ms (1%)

simplify47.0ms (0.5%)

prune212.0ms (2%)

localize18.0ms (0.2%)

series238.0ms (2.3%)

rewrite83.0ms (0.8%)

simplify64.0ms (0.6%)

prune315.0ms (3%)

localize21.0ms (0.2%)

series230.0ms (2.2%)

rewrite119.0ms (1.1%)

simplify63.0ms (0.6%)

prune213.0ms (2%)

localize13.0ms (0.1%)

series124.0ms (1.2%)

rewrite76.0ms (0.7%)

simplify58.0ms (0.6%)

prune341.0ms (3.3%)

regimes1.6s (15.8%)

simplify3.0ms (0%)

end392.0ms (3.7%)

Profiling