Details

analyze76.0ms (1%)

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)

sample142.0ms (1.8%)

Algorithm

1×

intervals

Results

69.0ms	71×	body	1024	valid
27.0ms	152×	body	128	valid
12.0ms	24×	body	512	valid
10.0ms	256×	pre	128	true
3.0ms	9×	body	256	valid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify14.0ms (0.2%)

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)

localize16.0ms (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))

series83.0ms (1%)

Counts

2 → 28

Calls

2 calls:

68.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
15.0ms	(*.f64 e (sin.f64 v))

rewrite17.0ms (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:

7.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
6.0ms	(*.f64 e (sin.f64 v))

simplify126.0ms (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

prune158.0ms (2%)

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)))
	29.4b	(/.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))
	1.0b	(/.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))
▶	0.1b	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
	29.6b	(/.f64 (.f64 (.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	0.9b	(/.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))

Compiler

Compiled 2019 to 1052 computations (47.9% saved)

localize17.0ms (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)))

series128.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

68.0ms	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
60.0ms	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))

rewrite26.0ms (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:

12.0ms	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
5.0ms	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))

simplify178.0ms (2.3%)

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

prune235.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	127	7	134

Error

0.0b

Counts

134 → 7

Alt Table

Status	Error	Program
	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	29.4b	(/.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))
▶	0.1b	(*.f64 e (/.f64 (neg.f64 (sin.f64 v)) (neg.f64 (fma.f64 e (cos.f64 v) 1))))
	29.6b	(/.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 (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))
	6.9b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 3382 to 1806 computations (46.6% saved)

localize19.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series129.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

67.0ms	(*.f64 e (/.f64 (neg.f64 (sin.f64 v)) (neg.f64 (fma.f64 e (cos.f64 v) 1))))
61.0ms	(/.f64 (neg.f64 (sin.f64 v)) (neg.f64 (fma.f64 e (cos.f64 v) 1)))

rewrite126.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

201×	`times-frac_binary64`
135×	`add-sqr-sqrt_binary64`
130×	`*-un-lft-identity_binary64`
130×	`add-cube-cbrt_binary64`
126×	`distribute-lft-neg-in_binary64`

Counts

2 → 262

Calls

2 calls:

47.0ms	(*.f64 e (/.f64 (neg.f64 (sin.f64 v)) (neg.f64 (fma.f64 e (cos.f64 v) 1))))
14.0ms	(/.f64 (neg.f64 (sin.f64 v)) (neg.f64 (fma.f64 e (cos.f64 v) 1)))

simplify375.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-def_binary64`
359×	`associate-/l*_binary64`
307×	`associate-r_binary64`
289×	`times-frac_binary64`
277×	`associate-l_binary64`

Counts

310 → 349

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	426	8517
1	1108	8171
2	4724	8153
3	5404	8153

prune600.0ms (7.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	348	1	349
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	348	8	356

Error

Counts

356 → 8

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	29.4b	(/.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))
✓	0.1b	(*.f64 e (/.f64 (neg.f64 (sin.f64 v)) (neg.f64 (fma.f64 e (cos.f64 v) 1))))
	29.6b	(/.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 (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))
	34.8b	(.f64 (.f64 e (sqrt.f64 (neg.f64 (sin.f64 v)))) (/.f64 (sqrt.f64 (neg.f64 (sin.f64 v))) (neg.f64 (fma.f64 e (cos.f64 v) 1))))
	6.9b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 9042 to 4477 computations (50.5% saved)

localize21.0ms (0.3%)

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)))

series110.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

67.0ms	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
43.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))

rewrite33.0ms (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:

9.0ms	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
5.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))

simplify232.0ms (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

prune293.0ms (3.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	182	7	189

Error

Counts

189 → 7

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 e (/.f64 (neg.f64 (sin.f64 v)) (neg.f64 (fma.f64 e (cos.f64 v) 1))))
	29.6b	(/.f64 (.f64 (.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	34.8b	(.f64 (.f64 e (sqrt.f64 (neg.f64 (sin.f64 v)))) (/.f64 (sqrt.f64 (neg.f64 (sin.f64 v))) (neg.f64 (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 (cbrt.f64 e) (cbrt.f64 e)) (/.f64 (fma.f64 e (cos.f64 v) 1) (.f64 (sin.f64 v) (cbrt.f64 e))))
	6.9b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 4236 to 2048 computations (51.7% saved)

regimes391.0ms (4.9%)

Accuracy

Total 0.1b remaining (81.3%)

Threshold costs 0.1b (81.3%)

Counts

73 → 1

Compiler

Compiled 3719 to 2432 computations (34.6% saved)

simplify5.0ms (0.1%)

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

end1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample4.4s (55%)

Algorithm

1×

intervals

Results

1.9s	1941×	body	1024	valid
751.0ms	4583×	body	128	valid
490.0ms	985×	body	512	valid
276.0ms	8000×	pre	128	true
175.0ms	488×	body	256	valid
6.0ms	3×	body	2048	valid

Compiler

Compiled 147 to 96 computations (34.7% saved)

Details

analyze76.0ms (1%)

sample142.0ms (1.8%)

simplify14.0ms (0.2%)

prune5.0ms (0.1%)

localize16.0ms (0.2%)

series83.0ms (1%)

rewrite17.0ms (0.2%)

simplify126.0ms (1.6%)

prune158.0ms (2%)

localize17.0ms (0.2%)

series128.0ms (1.6%)

rewrite26.0ms (0.3%)

simplify178.0ms (2.3%)

prune235.0ms (3%)

localize19.0ms (0.2%)

series129.0ms (1.6%)

rewrite126.0ms (1.6%)

simplify375.0ms (4.7%)

prune600.0ms (7.6%)

localize21.0ms (0.3%)

series110.0ms (1.4%)

rewrite33.0ms (0.4%)

simplify232.0ms (2.9%)

prune293.0ms (3.7%)

regimes391.0ms (4.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample4.4s (55%)

Profiling