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 (60.7%)

Results

1.4s	2023×	body	1024	valid
735.0ms	4659×	body	128	valid
452.0ms	1039×	body	512	valid
163.0ms	531×	body	256	valid
6.0ms	4×	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))

series38.0ms (0.8%)

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 (0.2%)

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))

simplify73.0ms (1.6%)

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

prune80.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	69	10	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	10	80

Error

0.0b

Counts

80 → 10

Alt Table

Status	Error	Program
	1.2b	(-.f64 (.f64 e (sin.f64 v)) (.f64 (cos.f64 v) (*.f64 (pow.f64 e 2) (sin.f64 v))))
	29.5b	(/.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))
	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))
	34.3b	(/.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)))
	1.1b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
▶	0.2b	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))

Compiler

Compiled 2117 to 1118 computations (47.2% saved)

localize7.0ms (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)))

series57.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

31.0ms	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
26.0ms	(/.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:

7.0ms	(*.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))

simplify99.0ms (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

prune135.0ms (2.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	127	10	137

Error

0.0b

Counts

137 → 10

Alt Table

Status	Error	Program
	1.0b	(.f64 e (.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))) (cbrt.f64 (/.f64 (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))
	1.2b	(.f64 e (-.f64 (sin.f64 v) (.f64 (cos.f64 v) (*.f64 e (sin.f64 v)))))
✓	0.2b	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
	29.5b	(/.f64 (.f64 (.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.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))
	34.3b	(/.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)))
	1.1b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))

Compiler

Compiled 3496 to 1872 computations (46.5% 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)))

series48.0ms (1%)

Counts

2 → 48

Calls

2 calls:

31.0ms	(/.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))

rewrite16.0ms (0.4%)

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))

simplify125.0ms (2.7%)

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

prune181.0ms (3.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	176	5	181
Fresh	4	4	8
Picked	0	1	1
Done	1	0	1
Total	181	10	191

Error

Counts

191 → 10

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)))
✓	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	9.5b	(/.f64 e (cbrt.f64 (pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) 3)))
	18.0b	(/.f64 e (log1p.f64 (expm1.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))
	29.5b	(/.f64 (.f64 (.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	1.0b	(.f64 e (.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))) (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	34.3b	(/.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))
▶	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
	1.1b	(/.f64 (*.f64 (cbrt.f64 e) (cbrt.f64 e)) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (cbrt.f64 e)))
	1.2b	(.f64 e (-.f64 (sin.f64 v) (.f64 (cos.f64 v) (*.f64 e (sin.f64 v)))))

Compiler

Compiled 4469 to 2188 computations (51% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series92.0ms (2%)

Counts

3 → 44

Calls

3 calls:

41.0ms	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
37.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e)))
13.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
42×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
38×	`add-cube-cbrt_binary64`
28×	`sqrt-prod_binary64`

Counts

3 → 121

Calls

3 calls:

7.0ms	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
4.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e)))
4.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))

simplify190.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
434×	`cancel-sign-sub-inv_binary64`
229×	`fma-neg_binary64`
214×	`associate-r_binary64`
148×	`unswap-sqr_binary64`

Counts

165 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	303	4872
1	789	4300
2	3050	4253
3	4840	4253
4	4952	4253
5	4997	4253
6	4946	4253

prune179.0ms (3.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	193	10	203

Error

Counts

203 → 10

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)))
✓	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	9.5b	(/.f64 e (cbrt.f64 (pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) 3)))
	18.0b	(/.f64 e (log1p.f64 (expm1.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))
	29.5b	(/.f64 (.f64 (.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	0.2b	(*.f64 (sin.f64 v) (/.f64 e (fma.f64 e (cos.f64 v) 1)))
	0.8b	(.f64 (.f64 (sin.f64 v) (fabs.f64 (cbrt.f64 e))) (/.f64 (sqrt.f64 (cbrt.f64 e)) (/.f64 (fma.f64 e (cos.f64 v) 1) (sqrt.f64 e))))
	1.0b	(.f64 e (.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))) (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	34.3b	(/.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))
✓	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))

Compiler

Compiled 5063 to 2207 computations (56.4% saved)

regimes261.0ms (5.6%)

Accuracy

Total 0.1b remaining (87.5%)

Threshold costs 0.1b (87.5%)

Counts

91 → 1

Compiler

Compiled 5180 to 3179 computations (38.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	13	15
2	12	15

end142.0ms (3.1%)

Compiler: Compiled 203 to 129 computations (36.5% saved)

Details

analyze23.0ms (0.5%)

sample2.8s (60.7%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series38.0ms (0.8%)

rewrite8.0ms (0.2%)

simplify73.0ms (1.6%)

prune80.0ms (1.7%)

localize7.0ms (0.2%)

series57.0ms (1.2%)

rewrite13.0ms (0.3%)

simplify99.0ms (2.1%)

prune135.0ms (2.9%)

localize7.0ms (0.2%)

series48.0ms (1%)

rewrite16.0ms (0.4%)

simplify125.0ms (2.7%)

prune181.0ms (3.9%)

localize9.0ms (0.2%)

series92.0ms (2%)

rewrite24.0ms (0.5%)

simplify190.0ms (4.1%)

prune179.0ms (3.9%)

regimes261.0ms (5.6%)

simplify2.0ms (0%)

end142.0ms (3.1%)

Profiling