Details

analyze1.6s (14.2%)

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 (34.9%)

Results

2.5s	3591×	body	1024	valid
545.0ms	1365×	body	512	valid
384.0ms	2453×	body	128	valid
321.0ms	214×	body	2048	valid
184.0ms	633×	body	256	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	256	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`
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

15.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.1b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))

Compiler

Compiled 45 to 28 computations (37.8% 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)))
✓	2.7b	(cos.f64 (+.f64 a b))

series72.0ms (0.6%)

Counts

3 → 52

Calls

3 calls:

43.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
24.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
5.0ms	(cos.f64 (+.f64 a b))

rewrite93.0ms (0.8%)

Algorithm

2×	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:

90.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
90.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
90.0ms	(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

simplify64.0ms (0.6%)

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

prune232.0ms (2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	156	16	172
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	16	173

Error

0.1b

Counts

173 → 16

Alt Table

Status	Error	Program
	15.9b	(.f64 r (.f64 (pow.f64 (cbrt.f64 (sin.f64 b)) 2) (*.f64 (cbrt.f64 (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a b))))))
	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))))))))
	15.1b	(/.f64 (*.f64 (sin.f64 b) r) (cos.f64 (+.f64 a b)))
	15.8b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) r)) 3)
	32.0b	(.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)) (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 3) (pow.f64 (cos.f64 b) 3)) (.f64 a a) (fma.f64 5/6 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 (sin.f64 b) 2)) (pow.f64 (cos.f64 b) 2)) (/.f64 (.f64 (pow.f64 a 3) (pow.f64 (sin.f64 b) 4)) (pow.f64 (cos.f64 b) 4))))))))
	15.2b	(*.f64 r (/.f64 (sin.f64 b) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (+.f64 a b)))) 1)))
	15.6b	(/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 (sin.f64 b) r)))
	22.7b	(.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))))))
	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 (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))))))
	15.2b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
	0.3b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 1 (.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 (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)))))))
▶	0.3b	(.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))))))
	36.5b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) r) 3))
	30.3b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (sqrt.f64 (cos.f64 (+.f64 a b)))) (sqrt.f64 (cos.f64 (+.f64 a b))))
	15.4b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (cbrt.f64 (cos.f64 (+.f64 a b))))

Compiler

Compiled 5288 to 1897 computations (64.1% 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 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)))))
✓	49.0b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series230.0ms (2%)

Counts

4 → 108

Calls

4 calls:

126.0ms	(.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))))))
71.0ms	(/.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)))
9.0ms	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))

rewrite81.0ms (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 → 111

Calls

4 calls:

78.0ms	(.f64 (sin.f64 b) (.f64 (sin.f64 a) 1))
78.0ms	(.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))))))
78.0ms	(/.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)))))
78.0ms	(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

simplify63.0ms (0.5%)

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 → 164

Iterations

Useful iterations: 2 (0.0ms)

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

prune330.0ms (2.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	199	4	203
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	203	16	219

Error

0.0b

Counts

219 → 16

Alt Table

Status	Error	Program
	15.9b	(.f64 r (.f64 (pow.f64 (cbrt.f64 (sin.f64 b)) 2) (*.f64 (cbrt.f64 (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a b))))))
	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 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (expm1.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))))))
	15.4b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (cbrt.f64 (cos.f64 (+.f64 a b))))
	0.3b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	15.6b	(/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 (sin.f64 b) r)))
	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 (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))))))
	15.2b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
	0.3b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 1 (.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 (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 (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) (log.f64 (pow.f64 (exp.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 (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)))))
	36.5b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) r) 3))
	15.8b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) r)) 3)
	15.2b	(*.f64 r (/.f64 (sin.f64 b) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (+.f64 a b)))) 1)))
	30.3b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (sqrt.f64 (cos.f64 (+.f64 a b)))) (sqrt.f64 (cos.f64 (+.f64 a b))))

Compiler

Compiled 7961 to 3293 computations (58.6% saved)

localize21.0ms (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 (log1p.f64 (expm1.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) (sin.f64 a))
✓	0.2b	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (expm1.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)))))
	49.0b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series208.0ms (1.8%)

Counts

3 → 76

Calls

3 calls:

127.0ms

(*.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (expm1.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))))))

71.0ms

(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (expm1.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)))))

10.0ms

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

rewrite77.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 89

Calls

3 calls:

74.0ms

(*.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (expm1.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))))))

74.0ms

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

74.0ms

(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (expm1.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)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	97
1	381	63
2	4322	63
3	5157	63
0	0	0
1	0	0

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

165 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	2250
1	491	2240
2	1755	2156
3	5494	2156

prune291.0ms (2.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	170	16	186

Error

0.0b

Counts

186 → 16

Alt Table

Status	Error	Program
	15.9b	(.f64 r (.f64 (pow.f64 (cbrt.f64 (sin.f64 b)) 2) (*.f64 (cbrt.f64 (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a b))))))
	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 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (expm1.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))))))
	15.4b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (cbrt.f64 (cos.f64 (+.f64 a b))))
	0.3b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	15.6b	(/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 (sin.f64 b) r)))
	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 (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))))))
	15.2b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
▶	0.3b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 1 (.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 (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 (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) (log.f64 (pow.f64 (exp.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 (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)))))
	36.5b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) r) 3))
	15.8b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) r)) 3)
	15.2b	(*.f64 r (/.f64 (sin.f64 b) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (+.f64 a b)))) 1)))
	30.3b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (sqrt.f64 (cos.f64 (+.f64 a b)))) (sqrt.f64 (cos.f64 (+.f64 a b))))

Compiler

Compiled 6352 to 2365 computations (62.8% 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 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 1 (.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 1 (.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)))))
	49.0b	(fma.f64 (neg.f64 (sin.f64 b)) (.f64 (sin.f64 a) 1) (.f64 (sin.f64 b) (*.f64 (sin.f64 a) 1)))

series202.0ms (1.8%)

Counts

2 → 60

Calls

2 calls:

128.0ms

(*.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 1 (*.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))))))

74.0ms

(/.f64 (sin.f64 b) (+.f64 (fma.f64 1 (*.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)))))

rewrite76.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

311×	`expm1-udef_binary64`
311×	`log1p-udef_binary64`
194×	`add-sqr-sqrt_binary64`
179×	`log1p-expm1-u_binary64`
179×	`expm1-log1p-u_binary64`

Counts

2 → 63

Calls

2 calls:

75.0ms

(*.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 1 (*.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))))))

74.0ms

(/.f64 (sin.f64 b) (+.f64 (fma.f64 1 (*.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)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	93
1	381	51
2	4433	51
3	5267	51
0	0	0
1	0	0

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-def_binary64`
550×	`associate-r_binary64`
535×	`associate-l_binary64`
444×	`associate-/r*_binary64`
196×	`associate-/r/_binary64`

Counts

123 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	1982
1	383	1980
2	1425	1920
3	5186	1920

prune347.0ms (3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	1	13	14
Picked	1	0	1
Done	0	1	1
Total	206	15	221

Error

0.0b

Counts

221 → 15

Alt Table

Status	Error	Program
	15.9b	(.f64 r (.f64 (pow.f64 (cbrt.f64 (sin.f64 b)) 2) (*.f64 (cbrt.f64 (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a b))))))
	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 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 1 (.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) (log.f64 (+.f64 1 (expm1.f64 (.f64 (sin.f64 b) (sin.f64 a)))))))))
	36.5b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) r) 3))
✓	0.3b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (log1p.f64 (expm1.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))))))
	15.4b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 2)) (cbrt.f64 (cos.f64 (+.f64 a b))))
	0.3b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	15.6b	(/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 (sin.f64 b) r)))
	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 (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))))))
	15.2b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
	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)))))))
	0.4b	(.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) (log.f64 (pow.f64 (exp.f64 (sin.f64 b)) (sin.f64 a)))))))
	15.8b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) r)) 3)
	15.2b	(*.f64 r (/.f64 (sin.f64 b) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (+.f64 a b)))) 1)))
	30.3b	(/.f64 (/.f64 (*.f64 (sin.f64 b) r) (sqrt.f64 (cos.f64 (+.f64 a b)))) (sqrt.f64 (cos.f64 (+.f64 a b))))

Compiler

Compiled 7260 to 3126 computations (56.9% saved)

regimes3.0s (25.9%)

Accuracy

Total 0.2b remaining (73.4%)

Threshold costs 0.2b (73.4%)

Counts

283 → 1

Compiler

Compiled 39501 to 24268 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	19	46
1	32	46
2	44	46
3	47	46
4	48	46
5	46	46

end325.0ms (2.8%)

Compiler: Compiled 490 to 271 computations (44.7% saved)

Details

analyze1.6s (14.2%)

sample4.0s (34.9%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series72.0ms (0.6%)

rewrite93.0ms (0.8%)

simplify64.0ms (0.6%)

prune232.0ms (2%)

localize18.0ms (0.2%)

series230.0ms (2%)

rewrite81.0ms (0.7%)

simplify63.0ms (0.5%)

prune330.0ms (2.9%)

localize21.0ms (0.2%)

series208.0ms (1.8%)

rewrite77.0ms (0.7%)

simplify60.0ms (0.5%)

prune291.0ms (2.5%)

localize18.0ms (0.2%)

series202.0ms (1.8%)

rewrite76.0ms (0.7%)

simplify52.0ms (0.5%)

prune347.0ms (3%)

regimes3.0s (25.9%)

simplify3.0ms (0%)

end325.0ms (2.8%)

Profiling