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 (63.3%)

Results

1.5s	2061×	body	1024	valid
752.0ms	4620×	body	128	valid
446.0ms	1050×	body	512	valid
154.0ms	522×	body	256	valid
5.0ms	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)

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))

series40.0ms (0.9%)

Counts

2 → 28

Calls

2 calls:

33.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
7.0ms	(*.f64 e (sin.f64 v))

rewrite51.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

58× egg-rr

Counts

2 → 58

Calls

2 calls:

50.0ms	((.f64 e (sin.f64 v)) (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	178	21
2	2238	21
3	5496	21
0	0	0
1	0	0

simplify55.0ms (1.2%)

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

86 → 89

Iterations

Useful iterations: 2 (0.0ms)

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

prune86.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	7	90

Error

0.0b

Counts

90 → 7

Alt Table

Status	Error	Program
	0.6b	(pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))) -1)
	29.8b	(/.f64 (-.f64 (+.f64 (.f64 v e) (.f64 1/120 (.f64 (pow.f64 v 5) e))) (.f64 1/6 (*.f64 (pow.f64 v 3) e))) (fma.f64 e (cos.f64 v) 1))
	1.1b	(.f64 (pow.f64 (cbrt.f64 (.f64 e (sin.f64 v))) 2) (.f64 (cbrt.f64 (.f64 e (sin.f64 v))) (/.f64 1 (fma.f64 e (cos.f64 v) 1))))
▶	0.1b	(.f64 e (.f64 (sin.f64 v) (/.f64 1 (fma.f64 e (cos.f64 v) 1))))
	0.2b	(*.f64 e (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
	34.9b	(/.f64 (cbrt.f64 (*.f64 (pow.f64 e 3) (pow.f64 (sin.f64 v) 3))) (fma.f64 e (cos.f64 v) 1))
	24.7b	(/.f64 (pow.f64 (sqrt.f64 (*.f64 e (sin.f64 v))) 2) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 2110 to 1175 computations (44.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series80.0ms (1.8%)

Counts

3 → 72

Calls

3 calls:

31.0ms	(.f64 e (.f64 (sin.f64 v) (/.f64 1 (fma.f64 e (cos.f64 v) 1))))
27.0ms	(*.f64 (sin.f64 v) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
22.0ms	(/.f64 1 (fma.f64 e (cos.f64 v) 1))

rewrite53.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

67× egg-rr

Counts

3 → 67

Calls

2 calls:

52.0ms	((.f64 e (.f64 (sin.f64 v) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))) (*.f64 (sin.f64 v) (/.f64 1 (fma.f64 e (cos.f64 v) 1))) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	201	37
2	2329	37
3	5510	37
0	0	0
1	0	0

simplify85.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

768×	`fma-def_binary64`
469×	`fma-neg_binary64`
421×	`cancel-sign-sub-inv_binary64`
202×	`neg-mul-1_binary64`
182×	`sub-neg_binary64`

Counts

139 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	2424
1	659	2341
2	2538	2292
3	4590	2292
4	5008	2292

prune149.0ms (3.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	134	5	139
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	136	10	146

Error

0.0b

Counts

146 → 10

Alt Table

Status	Error	Program
	29.8b	(/.f64 (-.f64 (+.f64 (.f64 v e) (.f64 1/120 (.f64 (pow.f64 v 5) e))) (.f64 1/6 (*.f64 (pow.f64 v 3) e))) (fma.f64 e (cos.f64 v) 1))
▶	0.2b	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	1.1b	(.f64 (pow.f64 (cbrt.f64 (.f64 e (sin.f64 v))) 2) (.f64 (cbrt.f64 (.f64 e (sin.f64 v))) (/.f64 1 (fma.f64 e (cos.f64 v) 1))))
	8.3b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	0.2b	(*.f64 e (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
	16.8b	(*.f64 e (log.f64 (exp.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	0.6b	(pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))) -1)
	1.0b	(*.f64 e (/.f64 (pow.f64 (cbrt.f64 (sin.f64 v)) 2) (/.f64 (fma.f64 e (cos.f64 v) 1) (cbrt.f64 (sin.f64 v)))))
	1.0b	(*.f64 e (pow.f64 (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) 3))
	24.7b	(/.f64 (pow.f64 (sqrt.f64 (*.f64 e (sin.f64 v))) 2) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 3668 to 2223 computations (39.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series132.0ms (2.9%)

Counts

4 → 96

Calls

4 calls:

46.0ms	(expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
30.0ms	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
28.0ms	(log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))
26.0ms	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))

rewrite60.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

114× egg-rr

Counts

4 → 114

Calls

2 calls:

58.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	53
1	195	53
2	2311	53
3	5632	53
0	0	0
1	0	0

simplify94.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

541×	`cancel-sign-sub-inv_binary64`
270×	`fma-neg_binary64`
241×	`sub-neg_binary64`
235×	`associate-r_binary64`
222×	`fma-def_binary64`

Counts

210 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	4002
1	825	3898
2	3375	3871
3	4999	3871

prune152.0ms (3.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	149	2	151
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	151	10	161

Error

0.0b

Counts

161 → 10

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (*.f64 (sin.f64 v) e) (fma.f64 e (cos.f64 v) 1))
	1.0b	(*.f64 e (/.f64 (pow.f64 (cbrt.f64 (sin.f64 v)) 2) (/.f64 (fma.f64 e (cos.f64 v) 1) (cbrt.f64 (sin.f64 v)))))
	29.8b	(/.f64 (-.f64 (+.f64 (.f64 v e) (.f64 1/120 (.f64 (pow.f64 v 5) e))) (.f64 1/6 (*.f64 (pow.f64 v 3) e))) (fma.f64 e (cos.f64 v) 1))
	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
✓	0.2b	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	1.1b	(.f64 (pow.f64 (cbrt.f64 (.f64 e (sin.f64 v))) 2) (.f64 (cbrt.f64 (.f64 e (sin.f64 v))) (/.f64 1 (fma.f64 e (cos.f64 v) 1))))
	8.3b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	0.6b	(pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))) -1)
	1.0b	(*.f64 e (pow.f64 (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) 3))
	24.7b	(/.f64 (pow.f64 (sqrt.f64 (*.f64 e (sin.f64 v))) 2) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 4506 to 2613 computations (42% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series39.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

31.0ms	(/.f64 (*.f64 (sin.f64 v) e) (fma.f64 e (cos.f64 v) 1))
7.0ms	(*.f64 (sin.f64 v) e)

rewrite50.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

58× egg-rr

Counts

2 → 58

Calls

2 calls:

49.0ms	((.f64 (sin.f64 v) e) (/.f64 (.f64 (sin.f64 v) e) (fma.f64 e (cos.f64 v) 1)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	178	21
2	2238	21
3	5496	21
0	0	0
1	0	0

simplify58.0ms (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

106 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	1103
1	345	1061
2	1320	1021
3	4791	1021
4	5067	1021

prune88.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	89	10	99

Error

0.0b

Counts

99 → 10

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (*.f64 (sin.f64 v) e) (fma.f64 e (cos.f64 v) 1))
	1.0b	(*.f64 e (/.f64 (pow.f64 (cbrt.f64 (sin.f64 v)) 2) (/.f64 (fma.f64 e (cos.f64 v) 1) (cbrt.f64 (sin.f64 v)))))
	29.8b	(/.f64 (-.f64 (+.f64 (.f64 v e) (.f64 1/120 (.f64 (pow.f64 v 5) e))) (.f64 1/6 (*.f64 (pow.f64 v 3) e))) (fma.f64 e (cos.f64 v) 1))
	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
✓	0.2b	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	1.1b	(.f64 (pow.f64 (cbrt.f64 (.f64 e (sin.f64 v))) 2) (.f64 (cbrt.f64 (.f64 e (sin.f64 v))) (/.f64 1 (fma.f64 e (cos.f64 v) 1))))
	8.3b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	0.6b	(pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))) -1)
	1.0b	(*.f64 e (pow.f64 (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) 3))
	24.7b	(/.f64 (pow.f64 (sqrt.f64 (*.f64 e (sin.f64 v))) 2) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 2034 to 1119 computations (45% saved)

regimes185.0ms (4.1%)

Accuracy

Total 0.1b remaining (74.1%)

Threshold costs 0.1b (74.1%)

Counts

69 → 1

Compiler

Compiled 2927 to 2054 computations (29.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	21	19
2	33	19
3	41	19
4	46	19
5	48	19
6	47	19

end142.0ms (3.1%)

Compiler: Compiled 194 to 134 computations (30.9% saved)

Details

analyze25.0ms (0.5%)

sample2.9s (63.3%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series40.0ms (0.9%)

rewrite51.0ms (1.1%)

simplify55.0ms (1.2%)

prune86.0ms (1.9%)

localize8.0ms (0.2%)

series80.0ms (1.8%)

rewrite53.0ms (1.2%)

simplify85.0ms (1.9%)

prune149.0ms (3.3%)

localize10.0ms (0.2%)

series132.0ms (2.9%)

rewrite60.0ms (1.3%)

simplify94.0ms (2.1%)

prune152.0ms (3.3%)

localize7.0ms (0.2%)

series39.0ms (0.8%)

rewrite50.0ms (1.1%)

simplify58.0ms (1.3%)

prune88.0ms (1.9%)

regimes185.0ms (4.1%)

simplify2.0ms (0.1%)

end142.0ms (3.1%)

Profiling