Details

analyze25.0ms (0.6%)

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 (65%)

Results

1.5s	2039×	body	1024	valid
755.0ms	4659×	body	128	valid
441.0ms	1048×	body	512	valid
152.0ms	504×	body	256	valid
8.0ms	6×	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))

series33.0ms (0.7%)

Counts

2 → 28

Calls

2 calls:

26.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
7.0ms	(*.f64 e (sin.f64 v))

rewrite10.0ms (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 (1.6%)

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

prune73.0ms (1.6%)

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)))
	33.7b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 e (sin.f64 v)) 3)) (fma.f64 e (cos.f64 v) 1))
	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))
▶	0.1b	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1)))) (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))))
	27.7b	(/.f64 (.f64 (.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 2031 to 1072 computations (47.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series46.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

26.0ms	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
20.0ms	(/.f64 1 (fma.f64 e (cos.f64 v) 1))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64`
18×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 73

Calls

2 calls:

6.0ms	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
2.0ms	(/.f64 1 (fma.f64 e (cos.f64 v) 1))

simplify73.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

670×	`associate-/r*_binary64`
524×	`fma-def_binary64`
281×	`cancel-sign-sub-inv_binary64`
216×	`associate-/r/_binary64`
204×	`associate-l_binary64`

Counts

121 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	2857
1	627	2629
2	2387	2592
3	5467	2592

prune161.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	177	7	184

Error

0.0b

Counts

184 → 7

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	33.7b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 e (sin.f64 v)) 3)) (fma.f64 e (cos.f64 v) 1))
	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))
✓	0.1b	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1)))) (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))))
	27.7b	(/.f64 (.f64 (.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 4367 to 2390 computations (45.3% saved)

localize7.0ms (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)))

series44.0ms (1%)

Counts

2 → 48

Calls

2 calls:

26.0ms	(/.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))

rewrite14.0ms (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))

simplify123.0ms (2.8%)

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

prune156.0ms (3.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	177	4	181
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	180	8	188

Error

Counts

188 → 8

Alt Table

Status	Error	Program
	17.1b	(/.f64 e (log1p.f64 (expm1.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))))
▶	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	8.0b	(/.f64 e (cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))) (/.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))))
✓	0.1b	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
	1.0b	(/.f64 (/.f64 e (*.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))))
	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1)))) (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))))
	27.7b	(/.f64 (.f64 (.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 4465 to 2176 computations (51.3% saved)

localize10.0ms (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))

series50.0ms (1.1%)

Counts

3 → 44

Calls

3 calls:

33.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
10.0ms	(*.f64 (sqrt.f64 e) (sin.f64 v))
8.0ms	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v)))

rewrite21.0ms (0.5%)

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:

6.0ms	(/.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)))
5.0ms	(*.f64 (sqrt.f64 e) (sin.f64 v))

simplify80.0ms (1.8%)

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

prune128.0ms (2.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	134	7	141

Error

Counts

141 → 7

Alt Table

Status	Error	Program
	8.0b	(/.f64 e (cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))) (/.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))))
	27.7b	(/.f64 (.f64 (.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.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))
✓	0.1b	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
	1.0b	(/.f64 (/.f64 e (*.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))))
	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1)))) (cbrt.f64 (/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))))

Compiler

Compiled 3242 to 1400 computations (56.8% saved)

regimes272.0ms (6.2%)

Accuracy

Total 0.1b remaining (79.8%)

Threshold costs 0.1b (79.8%)

Counts

99 → 1

Compiler

Compiled 5162 to 3230 computations (37.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	14	18
2	13	18

end116.0ms (2.6%)

Compiler: Compiled 197 to 117 computations (40.6% saved)

Details

analyze25.0ms (0.6%)

sample2.9s (65%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series33.0ms (0.7%)

rewrite10.0ms (0.2%)

simplify69.0ms (1.6%)

prune73.0ms (1.6%)

localize8.0ms (0.2%)

series46.0ms (1.1%)

rewrite13.0ms (0.3%)

simplify73.0ms (1.6%)

prune161.0ms (3.6%)

localize7.0ms (0.2%)

series44.0ms (1%)

rewrite14.0ms (0.3%)

simplify123.0ms (2.8%)

prune156.0ms (3.5%)

localize10.0ms (0.2%)

series50.0ms (1.1%)

rewrite21.0ms (0.5%)

simplify80.0ms (1.8%)

prune128.0ms (2.9%)

regimes272.0ms (6.2%)

simplify2.0ms (0%)

end116.0ms (2.6%)

Profiling