Details

analyze23.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
12.5%	12.5%	75%	2
12.5%	12.5%	75%	3
18.7%	6.2%	75%	4
21.8%	3.1%	75%	5
23.4%	1.6%	75%	6
23.4%	1.6%	75%	7
24.2%	0.8%	75%	8
24.2%	0.8%	75%	9
24.6%	0.4%	75%	10
24.6%	0.4%	75%	11
24.8%	0.2%	75%	12
24.8%	0.2%	75%	13
24.9%	0.1%	75%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample91.0ms (1.9%)

Algorithm

1×

intervals

Results

35.0ms	67×	body	1024	valid
13.0ms	144×	body	128	valid
9.0ms	34×	body	512	valid
6.0ms	256×	pre	128	true
2.0ms	11×	body	256	valid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`
2×	`fma-def_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	17	15
2	23	15
3	26	15
4	27	15
5	26	15

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 47 to 28 computations (40.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(*.f64 e (sin.f64 v))

series40.0ms (0.8%)

Counts

2 → 28

Calls

2 calls:

32.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
8.0ms	(*.f64 e (sin.f64 v))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

4.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
3.0ms	(*.f64 e (sin.f64 v))

simplify74.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

590×	`associate-/r*_binary64`
466×	`fma-def_binary64`
433×	`fma-neg_binary64`
287×	`associate-/r/_binary64`
260×	`associate-/l/_binary64`

Counts

71 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	1682
1	475	1537
2	1911	1497
3	4795	1497
4	5052	1497

prune82.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	71	8	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	9	80

Error

0.0b

Counts

80 → 9

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	35.5b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 e (sin.f64 v)) 3)) (fma.f64 e (cos.f64 v) 1))
	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	1.0b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
▶	0.1b	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
	0.1b	(*.f64 (/.f64 e (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 (sin.f64 v) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))))
	1.0b	(/.f64 (.f64 (.f64 e (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (cbrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 2037 to 1086 computations (46.7% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))

series62.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

33.0ms	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
29.0ms	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

2 → 63

Calls

2 calls:

5.0ms	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
4.0ms	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))

simplify98.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

646×	`fma-def_binary64`
406×	`fma-neg_binary64`
299×	`cancel-sign-sub-inv_binary64`
215×	`associate-/l/_binary64`
174×	`associate-r_binary64`

Counts

111 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	3054
1	671	2888
2	2604	2844
3	4630	2844
4	5015	2844

prune128.0ms (2.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	127	9	136

Error

0.0b

Counts

136 → 9

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	16.4b	(*.f64 e (log.f64 (exp.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	0.2b	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	0.1b	(*.f64 e (expm1.f64 (log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	1.0b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
▶	0.1b	(*.f64 (/.f64 e (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 (sin.f64 v) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))))
	1.0b	(/.f64 (.f64 (.f64 e (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (cbrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 3406 to 1838 computations (46% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sin.f64 v) (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))
✓	0.0b	(/.f64 e (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))
✓	0.0b	(sqrt.f64 (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(*.f64 (/.f64 e (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 (sin.f64 v) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))))

series184.0ms (3.9%)

Counts

4 → 72

Calls

4 calls:

67.0ms	(/.f64 (sin.f64 v) (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))
60.0ms	(/.f64 e (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))
33.0ms	(*.f64 (/.f64 e (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 (sin.f64 v) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))))
24.0ms	(sqrt.f64 (fma.f64 e (cos.f64 v) 1))

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`add-sqr-sqrt_binary64`
84×	`times-frac_binary64`
61×	`*-un-lft-identity_binary64`
61×	`add-cube-cbrt_binary64`
51×	`sqrt-prod_binary64`

Counts

4 → 172

Calls

4 calls:

14.0ms	(*.f64 (/.f64 e (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 (sin.f64 v) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))))
3.0ms	(/.f64 (sin.f64 v) (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))
3.0ms	(/.f64 e (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))
1.0ms	(sqrt.f64 (fma.f64 e (cos.f64 v) 1))

simplify152.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

381×	`associate-r_binary64`
329×	`associate-l_binary64`
307×	`fma-neg_binary64`
273×	`*-commutative_binary64`
258×	`fma-def_binary64`

Counts

244 → 282

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	414	7405
1	1183	6639
2	4241	6628
3	5131	6628

prune379.0ms (7.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	315	0	315
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	315	9	324

Error

0.0b

Counts

324 → 9

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	16.4b	(*.f64 e (log.f64 (exp.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	0.2b	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
▶	0.1b	(*.f64 e (expm1.f64 (log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	1.0b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
✓	0.1b	(*.f64 (/.f64 e (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 (sin.f64 v) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))))
	1.0b	(/.f64 (.f64 (.f64 e (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (cbrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 10353 to 5976 computations (42.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(*.f64 e (expm1.f64 (log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
✓	0.1b	(expm1.f64 (log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))
✓	0.3b	(log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))

series449.0ms (9.4%)

Counts

3 → 72

Calls

3 calls:

387.0ms

(log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))

32.0ms

(*.f64 e (expm1.f64 (log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))

29.0ms

(expm1.f64 (log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 42

Calls

3 calls:

4.0ms

(*.f64 e (expm1.f64 (log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))

0.0ms

(log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))

0.0ms

(expm1.f64 (log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))

simplify90.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

418×	`cancel-sign-sub-inv_binary64`
268×	`unswap-sqr_binary64`
258×	`sub-neg_binary64`
213×	`associate-r_binary64`
187×	`times-frac_binary64`

Counts

114 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	3945
1	854	3796
2	3570	3769
3	5030	3769

prune197.0ms (4.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	188	9	197

Error

0.0b

Counts

197 → 9

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	16.4b	(*.f64 e (log.f64 (exp.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	0.2b	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
✓	0.1b	(*.f64 e (expm1.f64 (log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	1.0b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
✓	0.1b	(*.f64 (/.f64 e (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 (sin.f64 v) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))))
	1.0b	(/.f64 (.f64 (.f64 e (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (cbrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 5798 to 3367 computations (41.9% saved)

regimes159.0ms (3.3%)

Accuracy

Total 0.1b remaining (69.4%)

Threshold costs 0.1b (69.4%)

Counts

56 → 1

Compiler

Compiled 2657 to 1688 computations (36.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	12	15
2	11	15

end0.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample2.5s (51.3%)

Algorithm

1×

intervals

Results

1.1s	2041×	body	1024	valid
402.0ms	4476×	body	128	valid
261.0ms	974×	body	512	valid
180.0ms	8000×	pre	128	true
93.0ms	503×	body	256	valid
7.0ms	6×	body	2048	valid

Compiler

Compiled 174 to 115 computations (33.9% saved)

Details

analyze23.0ms (0.5%)

sample91.0ms (1.9%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series40.0ms (0.8%)

rewrite9.0ms (0.2%)

simplify74.0ms (1.5%)

prune82.0ms (1.7%)

localize8.0ms (0.2%)

series62.0ms (1.3%)

rewrite13.0ms (0.3%)

simplify98.0ms (2.1%)

prune128.0ms (2.7%)

localize13.0ms (0.3%)

series184.0ms (3.9%)

rewrite38.0ms (0.8%)

simplify152.0ms (3.2%)

prune379.0ms (7.9%)

localize11.0ms (0.2%)

series449.0ms (9.4%)

rewrite6.0ms (0.1%)

simplify90.0ms (1.9%)

prune197.0ms (4.1%)

regimes159.0ms (3.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.5s (51.3%)

Profiling