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 (61.3%)

Results

1.5s	2062×	body	1024	valid
723.0ms	4641×	body	128	valid
438.0ms	1029×	body	512	valid
154.0ms	518×	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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 v)
✓	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

3 → 32

Calls

3 calls:

31.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
7.0ms	(*.f64 e (sin.f64 v))
2.0ms	(cos.f64 v)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 52

Calls

3 calls:

3.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
3.0ms	(*.f64 e (sin.f64 v))
1.0ms	(cos.f64 v)

simplify57.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

593×	`associate-/r*_binary64`
503×	`fma-def_binary64`
289×	`cancel-sign-sub-inv_binary64`
287×	`associate-/r/_binary64`
260×	`associate-/l/_binary64`

Counts

84 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	1787
1	522	1642
2	2032	1598
3	5006	1598

prune89.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	88	8	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	8	97

Error

0.0b

Counts

97 → 8

Alt Table

Status	Error	Program
	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))
	0.4b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (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)))
	0.3b	(/.f64 e (/.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))
	20.0b	(/.f64 (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (sqrt.f64 (*.f64 e (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 2309 to 1203 computations (47.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series58.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
29.0ms	(/.f64 (sin.f64 v) (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-r_binary64`

Counts

2 → 63

Calls

2 calls:

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

simplify101.0ms (2.2%)

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

prune141.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	143	9	152

Error

0.0b

Counts

152 → 9

Alt Table

Status	Error	Program
	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))
	0.4b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	13.1b	(*.f64 e (log.f64 (exp.f64 (/.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)))
▶	0.3b	(/.f64 e (/.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))
	20.0b	(/.f64 (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (sqrt.f64 (*.f64 e (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 3696 to 1982 computations (46.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 v)
✓	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)))

series48.0ms (1%)

Counts

2 → 48

Calls

2 calls:

31.0ms	(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
17.0ms	(/.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))

simplify121.0ms (2.6%)

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

prune191.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	198	9	207

Error

Counts

207 → 9

Alt Table

Status	Error	Program
	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))
▶	0.4b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	13.1b	(*.f64 e (log.f64 (exp.f64 (/.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)))
	5.7b	(/.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 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	20.0b	(/.f64 (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (sqrt.f64 (*.f64 e (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 4719 to 2312 computations (51% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 v)
	0.1b	(*.f64 e (sin.f64 v))
✓	0.2b	(/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v)))
✓	0.3b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))

series53.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

30.0ms	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
23.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v)))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 81

Calls

2 calls:

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

simplify100.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

487×	`fma-def_binary64`
422×	`associate-/r/_binary64`
372×	`fma-neg_binary64`
266×	`associate-/l/_binary64`
259×	`cancel-sign-sub-inv_binary64`

Counts

129 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	3325
1	569	2984
2	2245	2923
3	4563	2923
4	4949	2923

prune174.0ms (3.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	182	9	191

Error

Counts

191 → 9

Alt Table

Status	Error	Program
	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))
✓	0.4b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (*.f64 (cbrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	13.1b	(*.f64 e (log.f64 (exp.f64 (/.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)))
	5.7b	(/.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 (.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
	20.0b	(/.f64 (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (sqrt.f64 (*.f64 e (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 4137 to 2224 computations (46.2% saved)

regimes374.0ms (8.1%)

Accuracy

Total 0.1b remaining (80.2%)

Threshold costs 0.1b (80.2%)

Counts

133 → 1

Compiler

Compiled 6833 to 4562 computations (33.2% 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

end124.0ms (2.7%)

Compiler: Compiled 195 to 114 computations (41.5% saved)

Details

analyze23.0ms (0.5%)

sample2.8s (61.3%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series40.0ms (0.9%)

rewrite9.0ms (0.2%)

simplify57.0ms (1.2%)

prune89.0ms (1.9%)

localize9.0ms (0.2%)

series58.0ms (1.3%)

rewrite11.0ms (0.2%)

simplify101.0ms (2.2%)

prune141.0ms (3.1%)

localize7.0ms (0.2%)

series48.0ms (1%)

rewrite16.0ms (0.3%)

simplify121.0ms (2.6%)

prune191.0ms (4.1%)

localize11.0ms (0.2%)

series53.0ms (1.1%)

rewrite13.0ms (0.3%)

simplify100.0ms (2.2%)

prune174.0ms (3.8%)

regimes374.0ms (8.1%)

simplify2.0ms (0%)

end124.0ms (2.7%)

Profiling