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)

sample2.8s (64.6%)

Results

1.4s	2001×	body	1024	valid
756.0ms	4689×	body	128	valid
428.0ms	1021×	body	512	valid
158.0ms	539×	body	256	valid
10.0ms	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

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)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series39.0ms (0.9%)

Counts

3 → 32

Calls

3 calls:

30.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
7.0ms	(*.f64 e (sin.f64 v))
2.0ms	(cos.f64 v)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

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

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

593×	`associate-/r*_binary64`
503×	`fma-def_binary64`
289×	`cancel-sign-sub-inv_binary64`
287×	`associate-/r/_binary64`
260×	`associate-/l/_binary64`

Counts

84 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	1787
1	522	1642
2	2032	1598
3	5006	1598

prune88.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	89	7	96
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	8	97

Error

0.0b

Counts

97 → 8

Alt Table

Status	Error	Program
	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))
	33.0b	(cbrt.f64 (.f64 (.f64 (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1)) (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))) (/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))))
	33.2b	(/.f64 (.f64 (.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (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))
	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	33.3b	(/.f64 (.f64 (.f64 (sqrt.f64 e) (sqrt.f64 (sin.f64 v))) (*.f64 (sqrt.f64 e) (sqrt.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)))

Compiler

Compiled 2317 to 1207 computations (47.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 v)
✓	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 (1.1%)

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))

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))

simplify126.0ms (2.9%)

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

prune175.0ms (4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	194	4	198
Fresh	4	2	6
Picked	0	1	1
Done	1	0	1
Total	199	7	206

Error

Counts

206 → 7

Alt Table

Status	Error	Program
	1.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))) (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))) (/.f64 e (cbrt.f64 (/.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)))
	0.7b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	0.4b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
▶	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	8.0b	(/.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)))))
	33.2b	(/.f64 (*.f64 e (sqrt.f64 (sin.f64 v))) (/.f64 (fma.f64 e (cos.f64 v) 1) (sqrt.f64 (sin.f64 v))))

Compiler

Compiled 4659 to 2288 computations (50.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 v)
✓	0.0b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
✓	0.2b	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v)))
✓	0.2b	(*.f64 (sqrt.f64 e) (sin.f64 v))

series63.0ms (1.4%)

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))
12.0ms	(*.f64 (sqrt.f64 e) (sin.f64 v))
9.0ms	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v)))

rewrite19.0ms (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:

6.0ms	(/.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))

simplify85.0ms (1.9%)

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

prune128.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	150	7	157

Error

Counts

157 → 7

Alt Table

Status	Error	Program
	0.7b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	0.4b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
▶	0.2b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 (cos.f64 v) e)))
✓	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	8.0b	(/.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)))))
	33.2b	(/.f64 (*.f64 e (sqrt.f64 (sin.f64 v))) (/.f64 (fma.f64 e (cos.f64 v) 1) (sqrt.f64 (sin.f64 v))))
✓	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))

Compiler

Compiled 3617 to 1564 computations (56.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series37.0ms (0.8%)

Counts

2 → 20

Calls

2 calls:

30.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 (cos.f64 v) e)))
7.0ms	(*.f64 (cos.f64 v) e)

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 → 45

Calls

2 calls:

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

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

526×	`associate-/r*_binary64`
489×	`fma-def_binary64`
383×	`fma-neg_binary64`
243×	`cancel-sign-sub-inv_binary64`
238×	`associate-/r/_binary64`

Counts

65 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	1630
1	546	1455
2	2024	1417
3	4846	1417
4	5085	1417

prune131.0ms (3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	148	7	155

Error

Counts

155 → 7

Alt Table

Status	Error	Program
	0.7b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	0.4b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
✓	0.2b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 (cos.f64 v) e)))
✓	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	8.0b	(/.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)))))
	33.2b	(/.f64 (*.f64 e (sqrt.f64 (sin.f64 v))) (/.f64 (fma.f64 e (cos.f64 v) 1) (sqrt.f64 (sin.f64 v))))
✓	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))

Compiler

Compiled 3154 to 1493 computations (52.7% saved)

regimes278.0ms (6.4%)

Accuracy

Total 0.1b remaining (80.3%)

Threshold costs 0.1b (80.3%)

Counts

91 → 1

Compiler

Compiled 5402 to 3185 computations (41% 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

end100.0ms (2.3%)

Compiler: Compiled 143 to 90 computations (37.1% saved)

Details

analyze23.0ms (0.5%)

sample2.8s (64.6%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series39.0ms (0.9%)

rewrite9.0ms (0.2%)

simplify56.0ms (1.3%)

prune88.0ms (2%)

localize8.0ms (0.2%)

series49.0ms (1.1%)

rewrite14.0ms (0.3%)

simplify126.0ms (2.9%)

prune175.0ms (4%)

localize10.0ms (0.2%)

series63.0ms (1.4%)

rewrite19.0ms (0.4%)

simplify85.0ms (1.9%)

prune128.0ms (2.9%)

localize9.0ms (0.2%)

series37.0ms (0.8%)

rewrite9.0ms (0.2%)

simplify71.0ms (1.6%)

prune131.0ms (3%)

regimes278.0ms (6.4%)

simplify2.0ms (0%)

end100.0ms (2.3%)

Profiling