Details

analyze37.0ms (0.9%)

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)

sample78.0ms (2%)

Algorithm

1×

intervals

Results

41.0ms	74×	body	1024	valid
13.0ms	145×	body	128	valid
5.0ms	256×	pre	128	true
5.0ms	20×	body	512	valid
3.0ms	17×	body	256	valid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify7.0ms (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

prune4.0ms (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))

series39.0ms (1%)

Counts

2 → 28

Calls

2 calls:

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

rewrite10.0ms (0.3%)

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:

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

simplify70.0ms (1.8%)

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

prune72.0ms (1.8%)

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
	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	34.9b	(/.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))
	0.7b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
▶	0.1b	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
	32.8b	(/.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))
	0.5b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 1997 to 1050 computations (47.4% saved)

localize8.0ms (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)))

series83.0ms (2.1%)

Counts

2 → 48

Calls

2 calls:

42.0ms	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
41.0ms	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))

rewrite12.0ms (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:

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

simplify97.0ms (2.5%)

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

prune113.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	125	9	134

Error

0.0b

Counts

134 → 9

Alt Table

Status	Error	Program
	32.8b	(/.f64 (.f64 (.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	7.7b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	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))
	16.8b	(*.f64 e (log.f64 (exp.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	0.7b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
✓	0.1b	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
	0.9b	(.f64 e (.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 (cbrt.f64 (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))))
	0.5b	(/.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)))

Compiler

Compiled 3426 to 1844 computations (46.2% saved)

localize8.0ms (0.2%)

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)))

series52.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

34.0ms	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
18.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))

rewrite16.0ms (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:

5.0ms	(/.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))

simplify122.0ms (3.1%)

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

prune157.0ms (4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	181	9	190

Error

Counts

190 → 9

Alt Table

Status	Error	Program
	32.8b	(/.f64 (.f64 (.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	7.7b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	0.7b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
✓	0.1b	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
	0.9b	(.f64 e (.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 (cbrt.f64 (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))))
	16.8b	(*.f64 e (log.f64 (exp.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
▶	0.5b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	17.8b	(/.f64 e (log1p.f64 (expm1.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))
✓	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))

Compiler

Compiled 4385 to 2146 computations (51.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series66.0ms (1.7%)

Counts

3 → 44

Calls

3 calls:

43.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
13.0ms	(*.f64 (sqrt.f64 e) (sin.f64 v))
10.0ms	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v)))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
10×	`*-un-lft-identity_binary64`

Counts

3 → 72

Calls

3 calls:

8.0ms	(*.f64 (sqrt.f64 e) (sin.f64 v))
7.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
6.0ms	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v)))

simplify83.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-def_binary64`
463×	`fma-neg_binary64`
330×	`cancel-sign-sub-inv_binary64`
321×	`associate-/l/_binary64`
214×	`associate-r_binary64`

Counts

116 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	2164
1	588	1939
2	2399	1885
3	4574	1885
4	4955	1885

prune106.0ms (2.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	134	8	142

Error

Counts

142 → 8

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
	0.5b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 e)) (.f64 (sqrt.f64 (sqrt.f64 e)) (*.f64 (sqrt.f64 e) (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	0.7b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	0.9b	(.f64 e (.f64 (/.f64 (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))) (sqrt.f64 (fma.f64 e (cos.f64 v) 1))) (/.f64 (cbrt.f64 (sin.f64 v)) (sqrt.f64 (fma.f64 e (cos.f64 v) 1)))))
	7.7b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
✓	0.5b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	17.8b	(/.f64 e (log1p.f64 (expm1.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))
✓	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))

Compiler

Compiled 3206 to 1388 computations (56.7% saved)

regimes187.0ms (4.8%)

Accuracy

Total 0.1b remaining (79.9%)

Threshold costs 0.1b (79.9%)

Counts

54 → 1

Compiler

Compiled 3011 to 1832 computations (39.2% saved)

simplify2.0ms (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

end0.0ms (0%)

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

sample2.4s (62.4%)

Algorithm

1×

intervals

Results

1.0s	2009×	body	1024	valid
408.0ms	4501×	body	128	valid
268.0ms	990×	body	512	valid
171.0ms	8000×	pre	128	true
97.0ms	494×	body	256	valid
7.0ms	6×	body	2048	valid

Compiler

Compiled 167 to 109 computations (34.7% saved)

Details

analyze37.0ms (0.9%)

sample78.0ms (2%)

simplify7.0ms (0.2%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series39.0ms (1%)

rewrite10.0ms (0.3%)

simplify70.0ms (1.8%)

prune72.0ms (1.8%)

localize8.0ms (0.2%)

series83.0ms (2.1%)

rewrite12.0ms (0.3%)

simplify97.0ms (2.5%)

prune113.0ms (2.9%)

localize8.0ms (0.2%)

series52.0ms (1.3%)

rewrite16.0ms (0.4%)

simplify122.0ms (3.1%)

prune157.0ms (4%)

localize9.0ms (0.2%)

series66.0ms (1.7%)

rewrite25.0ms (0.6%)

simplify83.0ms (2.1%)

prune106.0ms (2.7%)

regimes187.0ms (4.8%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample2.4s (62.4%)

Profiling