Details

analyze23.0ms (0.4%)

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)

sample93.0ms (1.8%)

Algorithm

1×

intervals

Results

35.0ms	70×	body	1024	valid
12.0ms	138×	body	128	valid
10.0ms	35×	body	512	valid
5.0ms	256×	pre	128	true
2.0ms	13×	body	256	valid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify6.0ms (0.1%)

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))

series39.0ms (0.7%)

Counts

2 → 28

Calls

2 calls:

31.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
7.0ms	(*.f64 e (sin.f64 v))

rewrite10.0ms (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))
4.0ms	(*.f64 e (sin.f64 v))

simplify69.0ms (1.3%)

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

prune72.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	72	7	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	7	80

Error

0.0b

Counts

80 → 7

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	22.8b	(/.f64 (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (sqrt.f64 (*.f64 e (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	31.0b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 e e) e) (.f64 (*.f64 (sin.f64 v) (sin.f64 v)) (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 e (sin.f64 v))) (cbrt.f64 (.f64 e (sin.f64 v)))) (cbrt.f64 (*.f64 e (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
▶	0.1b	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))

Compiler

Compiled 2019 to 1056 computations (47.7% saved)

localize7.0ms (0.1%)

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)))

series60.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
28.0ms	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))

rewrite13.0ms (0.2%)

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:

6.0ms	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
3.0ms	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))

simplify96.0ms (1.8%)

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

prune116.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	125	9	134

Error

Counts

134 → 9

Alt Table

Status	Error	Program
	1.1b	(.f64 e (.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 (cbrt.f64 (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))))
✓	0.1b	(*.f64 e (/.f64 (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))
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	22.8b	(/.f64 (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (sqrt.f64 (*.f64 e (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	31.0b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 e e) e) (.f64 (*.f64 (sin.f64 v) (sin.f64 v)) (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 e (sin.f64 v))) (cbrt.f64 (.f64 e (sin.f64 v)))) (cbrt.f64 (*.f64 e (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
▶	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	5.7b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))

Compiler

Compiled 3466 to 1852 computations (46.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))
✓	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))

series49.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

31.0ms	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
18.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 101

Calls

2 calls:

6.0ms	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
2.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))

simplify123.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

565×	`associate-/r/_binary64`
530×	`fma-def_binary64`
425×	`associate-/l/_binary64`
345×	`fma-neg_binary64`
299×	`cancel-sign-sub-inv_binary64`

Counts

149 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	285	4112
1	711	3934
2	2536	3870
3	5000	3870
4	5207	3870

prune156.0ms (3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	5	2	7
Picked	0	1	1
Done	0	1	1
Total	183	7	190

Error

Counts

190 → 7

Alt Table

Status	Error	Program
	29.6b	(*.f64 (sqrt.f64 (sin.f64 v)) (/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sqrt.f64 (sin.f64 v)))))
	22.8b	(/.f64 (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (sqrt.f64 (*.f64 e (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	5.6b	(/.f64 e (cbrt.f64 (pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) 3)))
	5.7b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
▶	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))
✓	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
✓	0.1b	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))

Compiler

Compiled 4311 to 2096 computations (51.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))
✓	0.3b	(/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e))
✓	0.3b	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))

series80.0ms (1.5%)

Counts

2 → 32

Calls

2 calls:

44.0ms	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))
36.0ms	(/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e))

rewrite187.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

1557×	`times-frac_binary64`
728×	`*-un-lft-identity_binary64`
728×	`add-sqr-sqrt_binary64`
728×	`add-cube-cbrt_binary64`
564×	`sqrt-prod_binary64`

Counts

2 → 713

Calls

2 calls:

22.0ms	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))
6.0ms	(/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e))

simplify657.0ms (12.7%)

Algorithm

1×	egg-herbie

Rules

562×	`associate-*r/_binary64`
512×	`associate-*l/_binary64`
444×	`associate-/r/_binary64`
391×	`associate-/l*_binary64`
348×	`fma-def_binary64`

Counts

745 → 851

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	788	34528
1	1860	32145
2	4804	32121
3	5124	32121

prune645.0ms (12.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	896	2	898
Fresh	2	2	4
Picked	0	1	1
Done	1	1	2
Total	899	6	905

Error

Counts

905 → 6

Alt Table

Status	Error	Program
	0.9b	(/.f64 (sqrt.f64 1) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
✓	0.1b	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
	5.6b	(/.f64 e (cbrt.f64 (pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) 3)))
	5.7b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
✓	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))
	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sqrt.f64 e) (sin.f64 v))))

Compiler

Compiled 29475 to 11647 computations (60.5% saved)

regimes208.0ms (4%)

Accuracy

Total 0.1b remaining (75.4%)

Threshold costs 0.1b (75.4%)

Counts

74 → 1

Compiler

Compiled 3689 to 2294 computations (37.8% saved)

simplify2.0ms (0%)

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)

sample2.4s (47%)

Algorithm

1×

intervals

Results

1.1s	2040×	body	1024	valid
420.0ms	4490×	body	128	valid
265.0ms	964×	body	512	valid
168.0ms	8000×	pre	128	true
96.0ms	503×	body	256	valid
4.0ms	3×	body	2048	valid

Compiler

Compiled 123 to 85 computations (30.9% saved)

Details

analyze23.0ms (0.4%)

sample93.0ms (1.8%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series39.0ms (0.7%)

rewrite10.0ms (0.2%)

simplify69.0ms (1.3%)

prune72.0ms (1.4%)

localize7.0ms (0.1%)

series60.0ms (1.2%)

rewrite13.0ms (0.2%)

simplify96.0ms (1.8%)

prune116.0ms (2.2%)

localize7.0ms (0.1%)

series49.0ms (0.9%)

rewrite16.0ms (0.3%)

simplify123.0ms (2.4%)

prune156.0ms (3%)

localize9.0ms (0.2%)

series80.0ms (1.5%)

rewrite187.0ms (3.6%)

simplify657.0ms (12.7%)

prune645.0ms (12.4%)

regimes208.0ms (4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.4s (47%)

Profiling