Details

analyze23.0ms (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)

sample2.8s (59.1%)

Results

1.5s	2102×	body	1024	valid
718.0ms	4589×	body	128	valid
432.0ms	1029×	body	512	valid
161.0ms	532×	body	256	valid
6.0ms	4×	body	2048	valid

Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify10.0ms (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

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 (0.1%)

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))

series31.0ms (0.6%)

Counts

2 → 28

Calls

2 calls:

24.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
6.0ms	(*.f64 e (sin.f64 v))

rewrite8.0ms (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:

4.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
3.0ms	(*.f64 e (sin.f64 v))

simplify68.0ms (1.4%)

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

prune75.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	71	8	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	8	80

Error

0.0b

Counts

80 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (sin.f64 v) (-.f64 e (.f64 (cos.f64 v) (*.f64 e e))))
	34.2b	(/.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 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))
▶	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	0.8b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	32.4b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 e e) e) (.f64 (*.f64 (sin.f64 v) (sin.f64 v)) (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	1.1b	(/.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))

Compiler

Compiled 2049 to 1076 computations (47.5% saved)

localize7.0ms (0.1%)

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)))

series40.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
16.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))

rewrite16.0ms (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))

simplify120.0ms (2.5%)

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

prune171.0ms (3.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	175	6	181
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	180	9	189

Error

0.0b

Counts

189 → 9

Alt Table

Status	Error	Program
	0.8b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
▶	0.1b	(*.f64 (/.f64 e (fma.f64 e (cos.f64 v) 1)) (sin.f64 v))
	1.0b	(.f64 (/.f64 (sqrt.f64 e) (/.f64 1 (.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))))) (/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (cbrt.f64 (sin.f64 v)))))
	34.2b	(*.f64 (sqrt.f64 (sin.f64 v)) (/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sqrt.f64 (sin.f64 v)))))
	1.1b	(.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (/.f64 (cbrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
	0.5b	(*.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.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)))
	32.4b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 e e) e) (.f64 (*.f64 (sin.f64 v) (sin.f64 v)) (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 4423 to 2158 computations (51.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series44.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

23.0ms	(*.f64 (/.f64 e (fma.f64 e (cos.f64 v) 1)) (sin.f64 v))
20.0ms	(/.f64 e (fma.f64 e (cos.f64 v) 1))

rewrite11.0ms (0.2%)

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-l_binary64`

Counts

2 → 63

Calls

2 calls:

5.0ms	(*.f64 (/.f64 e (fma.f64 e (cos.f64 v) 1)) (sin.f64 v))
2.0ms	(/.f64 e (fma.f64 e (cos.f64 v) 1))

simplify71.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

782×	`associate-/r*_binary64`
519×	`fma-def_binary64`
299×	`cancel-sign-sub-inv_binary64`
276×	`associate-/r/_binary64`
184×	`unswap-sqr_binary64`

Counts

111 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	242	2781
1	647	2619
2	2331	2575
3	5661	2575

prune126.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	136	8	144

Error

0.0b

Counts

144 → 8

Alt Table

Status	Error	Program
	0.8b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
✓	0.1b	(*.f64 (/.f64 e (fma.f64 e (cos.f64 v) 1)) (sin.f64 v))
	1.0b	(.f64 (/.f64 (sqrt.f64 e) (/.f64 1 (.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))))) (/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (cbrt.f64 (sin.f64 v)))))
	34.2b	(*.f64 (sqrt.f64 (sin.f64 v)) (/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sqrt.f64 (sin.f64 v)))))
▶	0.2b	(*.f64 (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) e)) (sin.f64 v))
✓	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	32.4b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 e e) e) (.f64 (*.f64 (sin.f64 v) (sin.f64 v)) (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 3438 to 1857 computations (46% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series53.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

25.0ms	(*.f64 (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) e)) (sin.f64 v))
19.0ms	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) e))
9.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) e)

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
103×	`add-sqr-sqrt_binary64`
91×	`*-un-lft-identity_binary64`
89×	`add-cube-cbrt_binary64`
44×	`associate-l_binary64`

Counts

3 → 181

Calls

3 calls:

11.0ms	(*.f64 (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) e)) (sin.f64 v))
4.0ms	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) e))
2.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) e)

simplify182.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-def_binary64`
394×	`cancel-sign-sub-inv_binary64`
306×	`fma-neg_binary64`
228×	`associate-r_binary64`
193×	`associate-l_binary64`

Counts

253 → 326

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	309	5567
1	772	5117
2	2902	5054
3	4480	5054
4	4983	5054
5	4947	5054

prune314.0ms (6.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	325	1	326
Fresh	0	5	5
Picked	0	1	1
Done	1	1	2
Total	326	8	334

Error

Counts

334 → 8

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
	0.5b	(*.f64 (/.f64 1 (sqrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) e))) (/.f64 (sin.f64 v) (sqrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) e))))
	0.8b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 (sin.f64 v) (sqrt.f64 e))))
	34.2b	(*.f64 (sqrt.f64 (sin.f64 v)) (/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sqrt.f64 (sin.f64 v)))))
✓	0.2b	(*.f64 (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) e)) (sin.f64 v))
	32.4b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 e e) e) (.f64 (*.f64 (sin.f64 v) (sin.f64 v)) (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
	1.0b	(.f64 (/.f64 (sqrt.f64 e) (/.f64 1 (.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))))) (/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (cbrt.f64 (sin.f64 v)))))

Compiler

Compiled 7993 to 4541 computations (43.2% saved)

regimes422.0ms (8.8%)

Accuracy

Total 0.1b remaining (83.1%)

Threshold costs 0.1b (83.1%)

Counts

145 → 1

Compiler

Compiled 8465 to 5522 computations (34.8% 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

end114.0ms (2.4%)

Compiler: Compiled 175 to 112 computations (36% saved)

Details

analyze23.0ms (0.5%)

sample2.8s (59.1%)

simplify10.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series31.0ms (0.6%)

rewrite8.0ms (0.2%)

simplify68.0ms (1.4%)

prune75.0ms (1.6%)

localize7.0ms (0.1%)

series40.0ms (0.8%)

rewrite16.0ms (0.3%)

simplify120.0ms (2.5%)

prune171.0ms (3.6%)

localize7.0ms (0.2%)

series44.0ms (0.9%)

rewrite11.0ms (0.2%)

simplify71.0ms (1.5%)

prune126.0ms (2.6%)

localize8.0ms (0.2%)

series53.0ms (1.1%)

rewrite33.0ms (0.7%)

simplify182.0ms (3.8%)

prune314.0ms (6.5%)

regimes422.0ms (8.8%)

simplify2.0ms (0%)

end114.0ms (2.4%)

Profiling