Details

analyze26.0ms (0.6%)

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 (64.9%)

Results

1.5s	2097×	body	1024	valid
725.0ms	4600×	body	128	valid
441.0ms	1050×	body	512	valid
147.0ms	504×	body	256	valid
7.0ms	5×	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

prune5.0ms (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)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series44.0ms (1%)

Counts

3 → 32

Calls

3 calls:

35.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
7.0ms	(*.f64 e (sin.f64 v))
2.0ms	(sin.f64 v)

rewrite10.0ms (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:

5.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
3.0ms	(*.f64 e (sin.f64 v))
1.0ms	(sin.f64 v)

simplify74.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

590×	`associate-/r*_binary64`
500×	`fma-def_binary64`
460×	`fma-neg_binary64`
310×	`cancel-sign-sub-inv_binary64`
287×	`associate-/r/_binary64`

Counts

84 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	1794
1	502	1638
2	1985	1594
3	4907	1594
4	5178	1594

prune91.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	89	7	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	7	97

Error

0.0b

Counts

97 → 7

Alt Table

Status	Error	Program
	0.2b	(/.f64 (*.f64 e (log1p.f64 (expm1.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))
	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	32.1b	(/.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))
	0.4b	(.f64 (sin.f64 v) (-.f64 (fma.f64 (pow.f64 (cos.f64 v) 2) (pow.f64 e 3) e) (fma.f64 (cos.f64 v) (.f64 e e) (*.f64 (pow.f64 (cos.f64 v) 3) (pow.f64 e 4)))))
	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))
▶	0.1b	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))

Compiler

Compiled 2281 to 1208 computations (47% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 v)
✓	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)))

series61.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
29.0ms	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))

rewrite11.0ms (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:

5.0ms	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
2.0ms	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))

simplify98.0ms (2.2%)

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

prune121.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	145	6	151

Error

0.0b

Counts

151 → 6

Alt Table

Status	Error	Program
	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	32.1b	(/.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))
▶	0.2b	(/.f64 (*.f64 e (log1p.f64 (expm1.f64 (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))
	0.4b	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (/.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)))

Compiler

Compiled 3584 to 1916 computations (46.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 e (log1p.f64 (expm1.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(*.f64 e (log1p.f64 (expm1.f64 (sin.f64 v))))
✓	0.2b	(expm1.f64 (sin.f64 v))
✓	0.2b	(log1p.f64 (expm1.f64 (sin.f64 v)))

series45.0ms (1%)

Counts

4 → 72

Calls

4 calls:

32.0ms	(/.f64 (*.f64 e (log1p.f64 (expm1.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
8.0ms	(*.f64 e (log1p.f64 (expm1.f64 (sin.f64 v))))
3.0ms	(expm1.f64 (sin.f64 v))
2.0ms	(log1p.f64 (expm1.f64 (sin.f64 v)))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

3.0ms	(/.f64 (*.f64 e (log1p.f64 (expm1.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
3.0ms	(*.f64 e (log1p.f64 (expm1.f64 (sin.f64 v))))
0.0ms	(expm1.f64 (sin.f64 v))
0.0ms	(log1p.f64 (expm1.f64 (sin.f64 v)))

simplify100.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

560×	`fma-def_binary64`
509×	`fma-neg_binary64`
348×	`cancel-sign-sub-inv_binary64`
287×	`associate-/r/_binary64`
260×	`associate-/l/_binary64`

Counts

137 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	2133
1	550	1960
2	2121	1905
3	4466	1905
4	4983	1905
5	4954	1905

prune102.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	146	6	152

Error

0.0b

Counts

152 → 6

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	32.1b	(/.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))
✓	0.2b	(/.f64 (*.f64 e (log1p.f64 (expm1.f64 (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))
	0.4b	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (/.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)))

Compiler

Compiled 3156 to 1505 computations (52.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 v)
✓	0.2b	(/.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)))

series54.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

33.0ms	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
20.0ms	(/.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 (2.8%)

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 (3.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	195	3	198
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	196	8	204

Error

Counts

204 → 8

Alt Table

Status	Error	Program
	1.2b	(/.f64 (*.f64 (cbrt.f64 e) (cbrt.f64 e)) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (cbrt.f64 e)))
	0.5b	(*.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
✓	0.2b	(/.f64 (*.f64 e (log1p.f64 (expm1.f64 (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))
✓	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	0.4b	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (/.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)))
	30.7b	(/.f64 (*.f64 e (sqrt.f64 (sin.f64 v))) (/.f64 (fma.f64 e (cos.f64 v) 1) (sqrt.f64 (sin.f64 v))))

Compiler

Compiled 4514 to 2194 computations (51.4% saved)

regimes250.0ms (5.7%)

Accuracy

Total 0.1b remaining (77.4%)

Threshold costs 0.1b (77.4%)

Counts

81 → 1

Compiler

Compiled 4088 to 2609 computations (36.2% 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

end107.0ms (2.4%)

Compiler: Compiled 149 to 94 computations (36.9% saved)

Details

analyze26.0ms (0.6%)

sample2.9s (64.9%)

simplify6.0ms (0.1%)

prune5.0ms (0.1%)

localize7.0ms (0.2%)

series44.0ms (1%)

rewrite10.0ms (0.2%)

simplify74.0ms (1.7%)

prune91.0ms (2.1%)

localize7.0ms (0.2%)

series61.0ms (1.4%)

rewrite11.0ms (0.2%)

simplify98.0ms (2.2%)

prune121.0ms (2.8%)

localize10.0ms (0.2%)

series45.0ms (1%)

rewrite9.0ms (0.2%)

simplify100.0ms (2.3%)

prune102.0ms (2.3%)

localize9.0ms (0.2%)

series54.0ms (1.2%)

rewrite14.0ms (0.3%)

simplify124.0ms (2.8%)

prune156.0ms (3.5%)

regimes250.0ms (5.7%)

simplify2.0ms (0%)

end107.0ms (2.4%)

Profiling