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)

sample2.9s (52.6%)

Results

1.5s	2154×	body	1024	valid
744.0ms	4621×	body	128	valid
415.0ms	968×	body	512	valid
157.0ms	507×	body	256	valid
8.0ms	6×	body	2048	valid

Compiler

Compiled 53 to 37 computations (30.2% 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

prune6.0ms (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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 47 to 28 computations (40.4% saved)

localize7.0ms (0.1%)

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))

series38.0ms (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))

rewrite8.0ms (0.1%)

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:

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

prune74.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	72	7	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	72	8	80

Error

0.0b

Counts

80 → 8

Alt Table

Status	Error	Program
	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))
	0.5b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.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))
	36.2b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 e (sin.f64 v)) 3)) (fma.f64 e (cos.f64 v) 1))
	31.5b	(-.f64 (fma.f64 (/.f64 v (+.f64 e 1)) e (fma.f64 1/120 (/.f64 (.f64 e (pow.f64 v 5)) (+.f64 e 1)) (fma.f64 1/2 (/.f64 (.f64 e (.f64 e (pow.f64 v 3))) (pow.f64 (+.f64 e 1) 2)) (.f64 1/4 (/.f64 (pow.f64 v 5) (pow.f64 (/.f64 (+.f64 e 1) e) 3)))))) (fma.f64 1/6 (/.f64 (.f64 e (pow.f64 v 3)) (+.f64 e 1)) (.f64 1/8 (/.f64 (.f64 e (.f64 e (pow.f64 v 5))) (pow.f64 (+.f64 e 1) 2)))))
▶	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	0.7b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
✓	0.2b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 2123 to 1154 computations (45.6% 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:

32.0ms	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
17.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))

rewrite15.0ms (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:

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

simplify117.0ms (2.1%)

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

prune144.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	182	7	189

Error

0.0b

Counts

189 → 7

Alt Table

Status	Error	Program
	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))
	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))
▶	0.5b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	36.2b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 e (sin.f64 v)) 3)) (fma.f64 e (cos.f64 v) 1))
✓	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	0.7b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	20.2b	(/.f64 e (log1p.f64 (expm1.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))

Compiler

Compiled 4327 to 2108 computations (51.3% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series61.0ms (1.1%)

Counts

3 → 44

Calls

3 calls:

41.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
11.0ms	(*.f64 (sqrt.f64 e) (sin.f64 v))
9.0ms	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v)))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
10×	`*-un-lft-identity_binary64`

Counts

3 → 72

Calls

3 calls:

8.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
6.0ms	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v)))
4.0ms	(*.f64 (sqrt.f64 e) (sin.f64 v))

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-def_binary64`
463×	`fma-neg_binary64`
330×	`cancel-sign-sub-inv_binary64`
321×	`associate-/l/_binary64`
214×	`associate-r_binary64`

Counts

116 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	2164
1	588	1939
2	2399	1885
3	4574	1885
4	4955	1885

prune102.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	133	7	140

Error

0.0b

Counts

140 → 7

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))
	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))
✓	0.5b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	36.2b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 e (sin.f64 v)) 3)) (fma.f64 e (cos.f64 v) 1))
✓	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	0.7b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	20.2b	(/.f64 e (log1p.f64 (expm1.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))

Compiler

Compiled 3261 to 1425 computations (56.3% 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 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))
✓	0.4b	(/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e))

series76.0ms (1.4%)

Counts

2 → 32

Calls

2 calls:

41.0ms	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))
35.0ms	(/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e))

rewrite169.0ms (3.1%)

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:

21.0ms	(/.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))

simplify629.0ms (11.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

745 → 836

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	788	33772
1	1860	32145
2	4805	32121
3	5124	32121

prune585.0ms (10.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	883	0	883
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	883	7	890

Error

0.0b

Counts

890 → 7

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))
	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))
✓	0.5b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	36.2b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 e (sin.f64 v)) 3)) (fma.f64 e (cos.f64 v) 1))
✓	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	0.7b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	20.2b	(/.f64 e (log1p.f64 (expm1.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))

Compiler

Compiled 29063 to 11501 computations (60.4% saved)

regimes201.0ms (3.7%)

Accuracy

Total 0.1b remaining (70.2%)

Threshold costs 0.1b (70.2%)

Counts

72 → 1

Compiler

Compiled 3806 to 2534 computations (33.4% 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

end97.0ms (1.8%)

Compiler: Compiled 132 to 86 computations (34.8% saved)

Details

analyze23.0ms (0.4%)

sample2.9s (52.6%)

simplify6.0ms (0.1%)

prune6.0ms (0.1%)

localize7.0ms (0.1%)

series38.0ms (0.7%)

rewrite8.0ms (0.1%)

simplify69.0ms (1.3%)

prune74.0ms (1.3%)

localize7.0ms (0.1%)

series49.0ms (0.9%)

rewrite15.0ms (0.3%)

simplify117.0ms (2.1%)

prune144.0ms (2.6%)

localize11.0ms (0.2%)

series61.0ms (1.1%)

rewrite21.0ms (0.4%)

simplify80.0ms (1.5%)

prune102.0ms (1.9%)

localize9.0ms (0.2%)

series76.0ms (1.4%)

rewrite169.0ms (3.1%)

simplify629.0ms (11.4%)

prune585.0ms (10.6%)

regimes201.0ms (3.7%)

simplify2.0ms (0%)

end97.0ms (1.8%)

Profiling