Details

analyze25.0ms (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)

sample2.9s (54.7%)

Results

1.5s	2061×	body	1024	valid
739.0ms	4620×	body	128	valid
446.0ms	1050×	body	512	valid
158.0ms	522×	body	256	valid
4.0ms	3×	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

0.1b

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)

localize9.0ms (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))

series37.0ms (0.7%)

Counts

2 → 28

Calls

2 calls:

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

rewrite138.0ms (2.6%)

Algorithm

2×	egg-rewrite

Rules

58×	`egg`
43×	`egg`

Counts

2 → 101

Calls

2 calls:

82.0ms	(*.f64 e (sin.f64 v))
54.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	97	6
2	1114	6
3	4736	6
4	6242	6
0	9	15
1	178	15
2	2238	15
3	5496	15

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

688×	`times-frac_binary64`
456×	`associate-/l*_binary64`
414×	`fma-neg_binary64`
404×	`fma-def_binary64`
359×	`associate-/r*_binary64`

Counts

129 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	983
1	345	941
2	1320	901
3	4791	901
4	5067	901

prune113.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	126	6	132
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	126	7	133

Error

Counts

133 → 7

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (sin.f64 v) (/.f64 (fma.f64 e (cos.f64 v) 1) e))
	32.1b	(/.f64 (.f64 (pow.f64 (sin.f64 v) 2/3) (.f64 (cbrt.f64 (sin.f64 v)) e)) (fma.f64 e (cos.f64 v) 1))
	0.4b	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))
	1.1b	(/.f64 (pow.f64 (cbrt.f64 (.f64 e (sin.f64 v))) 2) (/.f64 (fma.f64 e (cos.f64 v) 1) (cbrt.f64 (.f64 e (sin.f64 v)))))
	17.7b	(/.f64 (cbrt.f64 (*.f64 e e)) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (cbrt.f64 e)))
	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 2770 to 1419 computations (48.8% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series40.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

30.0ms	(/.f64 (sin.f64 v) (/.f64 (fma.f64 e (cos.f64 v) 1) e))
10.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) e)

rewrite135.0ms (2.6%)

Algorithm

2×	egg-rewrite

Rules

60×	`egg`
46×	`egg`

Counts

2 → 106

Calls

2 calls:

86.0ms	(/.f64 (sin.f64 v) (/.f64 (fma.f64 e (cos.f64 v) 1) e))
46.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) e)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	184	15
2	2400	15
3	4944	15
4	5587	15
0	7	10
1	137	10
2	1647	10
3	5189	10

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

677×	`times-frac_binary64`
422×	`associate-/l*_binary64`
364×	`fma-neg_binary64`
363×	`associate-/r*_binary64`
348×	`fma-def_binary64`

Counts

154 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1164
1	365	1114
2	1342	1080
3	4838	1080
4	5080	1080

prune117.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	145	6	151

Error

Counts

151 → 6

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))
	17.7b	(/.f64 (cbrt.f64 (*.f64 e e)) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (cbrt.f64 e)))
	1.0b	(/.f64 (pow.f64 (cbrt.f64 (sin.f64 v)) 2) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) e) (cbrt.f64 (sin.f64 v))))
✓	0.2b	(/.f64 (sin.f64 v) (/.f64 (fma.f64 e (cos.f64 v) 1) e))
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
	0.5b	(/.f64 (sin.f64 v) (pow.f64 (sqrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) e)) 2))

Compiler

Compiled 2849 to 1573 computations (44.8% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))
✓	0.3b	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))
✓	0.3b	(/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e))

series93.0ms (1.8%)

Counts

3 → 56

Calls

3 calls:

41.0ms	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))
35.0ms	(/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e))
17.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))

rewrite243.0ms (4.7%)

Algorithm

3×	egg-rewrite

Rules

69×	`egg`
58×	`egg`
43×	`egg`

Counts

3 → 170

Calls

3 calls:

97.0ms	(/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e))
78.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))
65.0ms	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	203	17
2	2619	17
3	4951	17
4	5568	17
0	11	22
1	229	15
2	3061	15
3	5577	15
0	8	12
1	156	12
2	1858	12
3	4980	12
4	4976	12

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

796×	`fma-def_binary64`
674×	`times-frac_binary64`
440×	`fma-neg_binary64`
425×	`cancel-sign-sub-inv_binary64`
148×	`sub-neg_binary64`

Counts

226 → 215

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	1606
1	499	1501
2	1901	1430
3	4586	1427
4	4964	1427

prune173.0ms (3.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	215	6	221

Error

Counts

221 → 6

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (*.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) (pow.f64 e -1/2))
✓	0.4b	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))
	17.7b	(/.f64 (cbrt.f64 (*.f64 e e)) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (cbrt.f64 e)))
	1.0b	(/.f64 (pow.f64 (cbrt.f64 (sin.f64 v)) 2) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) e) (cbrt.f64 (sin.f64 v))))
✓	0.2b	(/.f64 (sin.f64 v) (/.f64 (fma.f64 e (cos.f64 v) 1) e))
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 4857 to 2495 computations (48.6% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))
✓	0.3b	(/.f64 (*.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) (pow.f64 e -1/2))
✓	0.3b	(*.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))

series132.0ms (2.5%)

Counts

3 → 56

Calls

3 calls:

56.0ms

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

48.0ms

(/.f64 (*.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) (pow.f64 e -1/2))

28.0ms

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

rewrite247.0ms (4.7%)

Algorithm

3×	egg-rewrite

Rules

61×	`egg`
50×	`egg`
43×	`egg`

Counts

3 → 154

Calls

3 calls:

104.0ms

(/.f64 (*.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) (pow.f64 e -1/2))

83.0ms

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

57.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	197	17
2	2368	17
3	5128	17
0	13	23
1	272	15
2	3396	15
3	4988	15
4	5683	15
0	8	12
1	156	12
2	1858	12
3	4980	12
4	4976	12

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

551×	`fma-neg_binary64`
428×	`cancel-sign-sub-inv_binary64`
205×	`associate-/r/_binary64`
202×	`neg-mul-1_binary64`
197×	`fma-def_binary64`

Counts

210 → 209

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	2164
1	669	2080
2	2626	2034
3	4567	2032
4	5039	2032

prune172.0ms (3.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	1	1	2
Picked	0	1	1
Done	1	2	3
Total	210	5	215

Error

Counts

215 → 5

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (*.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) (pow.f64 e -1/2))
	0.4b	(/.f64 (/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))) (pow.f64 e -1/2))
	17.7b	(/.f64 (cbrt.f64 (*.f64 e e)) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (cbrt.f64 e)))
✓	0.2b	(/.f64 (sin.f64 v) (/.f64 (fma.f64 e (cos.f64 v) 1) e))
✓	0.1b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 5440 to 3147 computations (42.2% saved)

regimes258.0ms (4.9%)

Accuracy

Total 0.1b remaining (68.2%)

Threshold costs 0.1b (68.2%)

Counts

92 → 1

Compiler

Compiled 4196 to 2897 computations (31% 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

end81.0ms (1.6%)

Compiler: Compiled 100 to 68 computations (32% saved)

Details

analyze25.0ms (0.5%)

sample2.9s (54.7%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series37.0ms (0.7%)

rewrite138.0ms (2.6%)

simplify65.0ms (1.3%)

prune113.0ms (2.2%)

localize9.0ms (0.2%)

series40.0ms (0.8%)

rewrite135.0ms (2.6%)

simplify69.0ms (1.3%)

prune117.0ms (2.2%)

localize10.0ms (0.2%)

series93.0ms (1.8%)

rewrite243.0ms (4.7%)

simplify81.0ms (1.6%)

prune173.0ms (3.3%)

localize12.0ms (0.2%)

series132.0ms (2.5%)

rewrite247.0ms (4.7%)

simplify96.0ms (1.8%)

prune172.0ms (3.3%)

regimes258.0ms (4.9%)

simplify2.0ms (0%)

end81.0ms (1.6%)

Profiling