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 (55.3%)

Results

1.5s	2061×	body	1024	valid
755.0ms	4643×	body	128	valid
428.0ms	1003×	body	512	valid
159.0ms	543×	body	256	valid
9.0ms	6×	body	2048	valid

Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify7.0ms (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

0.1b

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 (0.1%)

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))

series40.0ms (0.8%)

Counts

2 → 28

Calls

2 calls:

32.0ms	(/.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:

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

prune67.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	73	6	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	7	80

Error

0.0b

Counts

80 → 7

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (*.f64 e (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)))
	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))
	30.8b	(/.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))
	1.1b	(/.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))
	34.1b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 e (sin.f64 v)) (.f64 e (sin.f64 v))) (*.f64 e (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 2015 to 1046 computations (48.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	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)))

series53.0ms (1%)

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))

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

simplify126.0ms (2.4%)

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 (3.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	173	8	181
Fresh	4	1	5
Picked	1	0	1
Done	0	1	1
Total	178	10	188

Error

Counts

188 → 10

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
	1.2b	(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
	31.2b	(/.f64 e (expm1.f64 (log1p.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))
▶	0.4b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
	30.7b	(/.f64 (*.f64 e (sqrt.f64 (sin.f64 v))) (/.f64 (fma.f64 e (cos.f64 v) 1) (sqrt.f64 (sin.f64 v))))
	0.9b	(/.f64 (/.f64 e (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))))) (/.f64 (fma.f64 e (cos.f64 v) 1) (cbrt.f64 (sin.f64 v))))
	0.9b	(/.f64 e (.f64 (.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)))) (cbrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))
	7.6b	(/.f64 e (cbrt.f64 (pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) 3)))
	0.9b	(.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)))))
	1.1b	(/.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))

Compiler

Compiled 4519 to 2214 computations (51% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e)))
✓	0.2b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
✓	0.3b	(*.f64 (sin.f64 v) (sqrt.f64 e))

series94.0ms (1.8%)

Counts

3 → 44

Calls

3 calls:

44.0ms	(/.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))

rewrite26.0ms (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:

8.0ms	(/.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))

simplify186.0ms (3.6%)

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 → 216

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

prune217.0ms (4.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	212	4	216
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	218	8	226

Error

Counts

226 → 8

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
	1.2b	(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
	1.3b	(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))) (sqrt.f64 e)))
▶	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))) (sqrt.f64 (sqrt.f64 e)))))
	1.1b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 (.f64 (sin.f64 v) (*.f64 (cbrt.f64 (sqrt.f64 e)) (cbrt.f64 (sqrt.f64 e)))) (cbrt.f64 (sqrt.f64 e)))))
	0.9b	(/.f64 (/.f64 e (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))))) (/.f64 (fma.f64 e (cos.f64 v) 1) (cbrt.f64 (sin.f64 v))))
	7.6b	(/.f64 e (cbrt.f64 (pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) 3)))
	0.5b	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 e)) (fma.f64 e (cos.f64 v) 1)) (.f64 (*.f64 (sqrt.f64 e) (sin.f64 v)) (sqrt.f64 (sqrt.f64 e))))

Compiler

Compiled 5766 to 2478 computations (57% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))) (sqrt.f64 (sqrt.f64 e))))
✓	0.2b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))) (sqrt.f64 (sqrt.f64 e)))))
✓	0.3b	(*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))
✓	0.4b	(.f64 (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))) (sqrt.f64 (sqrt.f64 e)))

series247.0ms (4.8%)

Counts

4 → 64

Calls

4 calls:

151.0ms	(*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))
45.0ms	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))) (sqrt.f64 (sqrt.f64 e)))))
38.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))) (sqrt.f64 (sqrt.f64 e))))
13.0ms	(.f64 (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))) (sqrt.f64 (sqrt.f64 e)))

rewrite49.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
49×	`add-sqr-sqrt_binary64`
45×	`sqrt-prod_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`

Counts

4 → 155

Calls

4 calls:

11.0ms	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))) (sqrt.f64 (sqrt.f64 e)))))
8.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))) (sqrt.f64 (sqrt.f64 e))))
7.0ms	(.f64 (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))) (sqrt.f64 (sqrt.f64 e)))
7.0ms	(*.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e)))

simplify133.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

551×	`cancel-sign-sub-inv_binary64`
351×	`associate-r_binary64`
266×	`fma-neg_binary64`
261×	`associate-l_binary64`
212×	`unswap-sqr_binary64`

Counts

219 → 265

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	349	5999
1	931	5153
2	3789	5142
3	5267	5142

prune229.0ms (4.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	265	0	265
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	265	8	273

Error

Counts

273 → 8

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
	1.2b	(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
	1.3b	(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))) (sqrt.f64 e)))
✓	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 (.f64 (sin.f64 v) (sqrt.f64 (sqrt.f64 e))) (sqrt.f64 (sqrt.f64 e)))))
	1.1b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 (.f64 (sin.f64 v) (*.f64 (cbrt.f64 (sqrt.f64 e)) (cbrt.f64 (sqrt.f64 e)))) (cbrt.f64 (sqrt.f64 e)))))
	0.9b	(/.f64 (/.f64 e (/.f64 1 (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))))) (/.f64 (fma.f64 e (cos.f64 v) 1) (cbrt.f64 (sin.f64 v))))
	7.6b	(/.f64 e (cbrt.f64 (pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) 3)))
	0.5b	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 e)) (fma.f64 e (cos.f64 v) 1)) (.f64 (*.f64 (sqrt.f64 e) (sin.f64 v)) (sqrt.f64 (sqrt.f64 e))))

Compiler

Compiled 7827 to 2895 computations (63% saved)

regimes393.0ms (7.6%)

Accuracy

Total 0.1b remaining (85.4%)

Threshold costs 0.1b (85.4%)

Counts

132 → 1

Compiler

Compiled 8222 to 5060 computations (38.5% 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

end118.0ms (2.3%)

Compiler: Compiled 173 to 107 computations (38.2% saved)

Details

analyze23.0ms (0.4%)

sample2.9s (55.3%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series40.0ms (0.8%)

rewrite8.0ms (0.2%)

simplify69.0ms (1.3%)

prune67.0ms (1.3%)

localize7.0ms (0.1%)

series53.0ms (1%)

rewrite15.0ms (0.3%)

simplify126.0ms (2.4%)

prune181.0ms (3.5%)

localize9.0ms (0.2%)

series94.0ms (1.8%)

rewrite26.0ms (0.5%)

simplify186.0ms (3.6%)

prune217.0ms (4.2%)

localize11.0ms (0.2%)

series247.0ms (4.8%)

rewrite49.0ms (0.9%)

simplify133.0ms (2.6%)

prune229.0ms (4.4%)

regimes393.0ms (7.6%)

simplify2.0ms (0%)

end118.0ms (2.3%)

Profiling