Metrics for math.cos on complex, real part

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample2.2s (87.9%)

Results

687.0ms	1009×	body	1024	valid
473.0ms	2525×	body	256	infinite
463.0ms	2691×	body	256	valid
316.0ms	1013×	body	1024	infinite
160.0ms	493×	body	512	valid
116.0ms	524×	body	512	infinite
1.0ms	1×	body	2048	valid

Bogosity

preprocess105.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1664×	`fma-def`
928×	`associate-/r/`
792×	`sqr-pow`
750×	`associate-/l/`
676×	`fabs-mul`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	140
1	81	140
2	182	140
3	343	132
4	674	132
5	1905	132
6	3540	132
7	3945	132
8	4964	132
9	5834	132
10	7272	132

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (cos.f64 (neg.f64 re))) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 (neg.f64 im))) (exp.f64 (neg.f64 im))))
(.f64 (.f64 1/2 (cos.f64 im)) (+.f64 (exp.f64 (neg.f64 re)) (exp.f64 re)))

Outputs
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 1/2 (.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (cos.f64 re)))
(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(.f64 (.f64 1/2 (cos.f64 (neg.f64 re))) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 1/2 (.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (cos.f64 re)))
(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 (neg.f64 im))) (exp.f64 (neg.f64 im))))
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 1/2 (.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (cos.f64 re)))
(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(.f64 (.f64 1/2 (cos.f64 im)) (+.f64 (exp.f64 (neg.f64 re)) (exp.f64 re)))
(*.f64 (cos.f64 im) (fma.f64 1/2 (exp.f64 re) (/.f64 1/2 (exp.f64 re))))

Symmetry

(abs re)

(abs im)

Compiler

Compiled 15 to 12 computations (20% saved)

simplify95.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1464×	`fma-def`
1028×	`associate-/l*`
860×	`unswap-sqr`
748×	`times-frac`
636×	`associate-/r/`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	30	35
2	73	35
3	132	33
4	194	33
5	348	33
6	790	33
7	1337	33
8	3879	33
9	4401	33
10	5368	33
11	5952	33
12	6984	33

Stop Event

1×	node limit

Counts

1 → 3

Calls

Call 1

Inputs
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Outputs

(*.f64 (*.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

(*.f64 1/2 (*.f64 (cos.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))

(*.f64 (cos.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

eval1.0ms (0%)

Compiler: Compiled 35 to 18 computations (48.6% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	2	1	3
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	2	2	4

Accurracy

100.0%

Counts

4 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
▶	100.0%	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize72.0ms (2.8%)

Compiler: Compiled 36 to 14 computations (61.1% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	0	0
Total	1	1

Accurracy

100.0%

Counts

1 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative`
4×	`+-commutative`
2×	`sub-neg`
2×	`neg-mul-1`
2×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	20	35
2	22	35
3	23	35

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Outputs
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 13 to 10 computations (23.1% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess27.0ms (1.1%)

Remove

(abs im)

(abs re)

Compiler

Compiled 104 to 80 computations (23.1% saved)

analyze0.0ms (0%)

sample2.2s (87.9%)

preprocess105.0ms (4.1%)

simplify95.0ms (3.8%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize72.0ms (2.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.2%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess27.0ms (1.1%)

Profiling