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)

sample3.0s (61.5%)

Results

1.6s	2148×	body	1024	valid
762.0ms	4589×	body	128	valid
447.0ms	1009×	body	512	valid
149.0ms	508×	body	256	valid
2.0ms	2×	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

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

0.2b

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 (0.2%)

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))

series33.0ms (0.7%)

Counts

2 → 28

Calls

2 calls:

24.0ms	(/.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:

5.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
3.0ms	(*.f64 e (sin.f64 v))

simplify70.0ms (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

prune79.0ms (1.6%)

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
	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	0.5b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
▶	0.1b	(/.f64 (/.f64 (*.f64 e (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (sqrt.f64 (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))
	0.3b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	23.7b	(/.f64 (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (sqrt.f64 (*.f64 e (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	33.1b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 e (sin.f64 v)) 3)) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 1997 to 1060 computations (46.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series77.0ms (1.6%)

Counts

2 → 40

Calls

2 calls:

51.0ms	(/.f64 (*.f64 e (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))
26.0ms	(/.f64 (/.f64 (*.f64 e (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
60×	`sqrt-prod_binary64`
49×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
49×	`add-cube-cbrt_binary64`

Counts

2 → 124

Calls

2 calls:

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

simplify129.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

444×	`associate-/r/_binary64`
444×	`cancel-sign-sub-inv_binary64`
188×	`fma-neg_binary64`
187×	`associate-r_binary64`
168×	`associate-l_binary64`

Counts

164 → 188

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	307	6341
1	839	5832
2	2909	5583
3	4955	5583

prune227.0ms (4.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	216	7	223

Error

0.0b

Counts

223 → 7

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	0.5b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	23.7b	(/.f64 (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))) (/.f64 (sqrt.f64 (fma.f64 e (cos.f64 v) 1)) (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))))))
✓	0.1b	(/.f64 (/.f64 (*.f64 e (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (sqrt.f64 (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))
	0.3b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	33.1b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 e (sin.f64 v)) 3)) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 7128 to 3999 computations (43.9% saved)

localize7.0ms (0.2%)

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)))

series50.0ms (1%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(/.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))

rewrite14.0ms (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)))
2.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))

simplify124.0ms (2.6%)

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

prune171.0ms (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	180	8	188

Error

0.0b

Counts

188 → 8

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	0.5b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	23.7b	(/.f64 (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))) (/.f64 (sqrt.f64 (fma.f64 e (cos.f64 v) 1)) (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))))))
✓	0.1b	(/.f64 (/.f64 (*.f64 e (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))
▶	0.3b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	1.0b	(/.f64 e (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (cbrt.f64 (sin.f64 v))))
	33.1b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 e (sin.f64 v)) 3)) (fma.f64 e (cos.f64 v) 1))
	7.0b	(/.f64 e (cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 e (cos.f64 v) 1) (fma.f64 e (cos.f64 v) 1)) (fma.f64 e (cos.f64 v) 1)) (.f64 (.f64 (sin.f64 v) (sin.f64 v)) (sin.f64 v)))))

Compiler

Compiled 4417 to 2155 computations (51.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series48.0ms (1%)

Counts

2 → 48

Calls

2 calls:

26.0ms	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
22.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v)))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
28×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`

Counts

2 → 81

Calls

2 calls:

5.0ms	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
3.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v)))

simplify102.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

487×	`fma-def_binary64`
422×	`associate-/r/_binary64`
372×	`fma-neg_binary64`
266×	`associate-/l/_binary64`
259×	`cancel-sign-sub-inv_binary64`

Counts

129 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	3325
1	569	2984
2	2245	2923
3	4563	2923
4	4949	2923

prune155.0ms (3.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	165	8	173

Error

Counts

173 → 8

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	0.5b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	23.7b	(/.f64 (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))) (/.f64 (sqrt.f64 (fma.f64 e (cos.f64 v) 1)) (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))))))
✓	0.1b	(/.f64 (/.f64 (*.f64 e (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))
✓	0.3b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	1.0b	(/.f64 e (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (cbrt.f64 (sin.f64 v))))
	33.1b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 e (sin.f64 v)) 3)) (fma.f64 e (cos.f64 v) 1))
	1.0b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 e (sin.f64 v)))) (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 e (sin.f64 v)))))) (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 e (sin.f64 v)))))

Compiler

Compiled 3837 to 2065 computations (46.2% saved)

regimes326.0ms (6.8%)

Accuracy

Total 0.1b remaining (81.1%)

Threshold costs 0.1b (81.1%)

Counts

109 → 1

Compiler

Compiled 6314 to 3917 computations (38% 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	11	28
1	14	28
2	13	28

end131.0ms (2.7%)

Compiler: Compiled 211 to 130 computations (38.4% saved)

Details

analyze23.0ms (0.5%)

sample3.0s (61.5%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series33.0ms (0.7%)

rewrite9.0ms (0.2%)

simplify70.0ms (1.5%)

prune79.0ms (1.6%)

localize9.0ms (0.2%)

series77.0ms (1.6%)

rewrite26.0ms (0.5%)

simplify129.0ms (2.7%)

prune227.0ms (4.7%)

localize7.0ms (0.2%)

series50.0ms (1%)

rewrite14.0ms (0.3%)

simplify124.0ms (2.6%)

prune171.0ms (3.6%)

localize9.0ms (0.2%)

series48.0ms (1%)

rewrite14.0ms (0.3%)

simplify102.0ms (2.1%)

prune155.0ms (3.2%)

regimes326.0ms (6.8%)

simplify2.0ms (0%)

end131.0ms (2.7%)

Profiling