Metrics for math.sin 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 15 to 12 computations (20% saved)

sample2.4s (82.2%)

Results

625.0ms	1009×	body	1024	valid
527.0ms	2612×	body	256	valid
398.0ms	2522×	body	256	infinite
388.0ms	1017×	body	1024	infinite
273.0ms	516×	body	512	infinite
171.0ms	577×	body	512	valid
3.0ms	3×	body	2048	valid

Bogosity

preprocess196.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

2266×	`fma-def`
1538×	`div-sub`
1052×	`times-frac`
902×	`distribute-lft-neg-in`
784×	`distribute-rgt-neg-in`

Problems

256×

No Errors

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	36	316
1	111	308
2	394	308
3	1005	298
4	2232	294
5	5131	294
6	7600	294

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (sin.f64 (neg.f64 re))) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 (neg.f64 im))) (exp.f64 (neg.f64 im))))
(neg.f64 (.f64 (.f64 1/2 (sin.f64 (neg.f64 re))) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
(neg.f64 (.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 (neg.f64 im))) (exp.f64 (neg.f64 im)))))
(.f64 (.f64 1/2 (sin.f64 im)) (+.f64 (exp.f64 (-.f64 0 re)) (exp.f64 re)))

Outputs
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(.f64 (.f64 1/2 (sin.f64 (neg.f64 re))) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
(.f64 1/2 (.f64 (neg.f64 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
(.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (.f64 (sin.f64 re) -1/2))
(.f64 (sin.f64 re) (.f64 -1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
(*.f64 (sin.f64 re) (fma.f64 (exp.f64 im) -1/2 (/.f64 -1/2 (exp.f64 im))))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 (neg.f64 im))) (exp.f64 (neg.f64 im))))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(neg.f64 (.f64 (.f64 1/2 (sin.f64 (neg.f64 re))) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
(neg.f64 (.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 (neg.f64 im))) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (neg.f64 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
(.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (.f64 (sin.f64 re) -1/2))
(.f64 (sin.f64 re) (.f64 -1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
(*.f64 (sin.f64 re) (fma.f64 (exp.f64 im) -1/2 (/.f64 -1/2 (exp.f64 im))))
(.f64 (.f64 1/2 (sin.f64 im)) (+.f64 (exp.f64 (-.f64 0 re)) (exp.f64 re)))
(.f64 (.f64 1/2 (sin.f64 im)) (+.f64 (exp.f64 (neg.f64 re)) (exp.f64 re)))
(.f64 (sin.f64 im) (.f64 1/2 (+.f64 (exp.f64 (neg.f64 re)) (exp.f64 re))))
(*.f64 (sin.f64 im) (fma.f64 1/2 (exp.f64 re) (/.f64 1/2 (exp.f64 re))))

Symmetry

(abs im)

(negabs re)

Compiler

Compiled 55 to 36 computations (34.5% saved)

eval1.0ms (0%)

Compiler: Compiled 24 to 15 computations (37.5% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize75.0ms (2.6%)

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

eval0.0ms (0%)

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

prune3.0ms (0.1%)

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

Accuracy

100.0%

Counts

1 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 38 to 27 computations (28.9% saved)

regimes17.0ms (0.6%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

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

Calls

6 calls:

4.0ms	im
3.0ms	(*.f64 1/2 (sin.f64 re))
2.0ms	(sin.f64 re)
2.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
2.0ms	re

Results

Accuracy	Segments	Branch
100.0%	1	`re`
100.0%	1	`im`
100.0%	1	`(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))`
100.0%	1	`(*.f64 1/2 (sin.f64 re))`
100.0%	1	`(sin.f64 re)`
100.0%	1	`(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))`

Compiler

Compiled 64 to 47 computations (26.6% saved)

simplify2.0ms (0.1%)

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	16	44
1	23	44
2	25	44
3	26	44

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 13 to 10 computations (23.1% saved)

soundness196.0ms (6.7%)

Rules

2266×	`fma-def`
1538×	`div-sub`
1052×	`times-frac`
902×	`distribute-lft-neg-in`
784×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	36	316
1	111	308
2	394	308
3	1005	298
4	2232	294
5	5131	294
6	7600	294

Stop Event

1×	node limit

Compiler

Compiled 100 to 57 computations (43% saved)

end0.0ms (0%)

preprocess30.0ms (1%)

Remove

(negabs re)

(abs im)

Compiler

Compiled 106 to 82 computations (22.6% saved)

analyze0.0ms (0%)

sample2.4s (82.2%)

preprocess196.0ms (6.7%)

eval1.0ms (0%)

prune1.0ms (0%)

localize75.0ms (2.6%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes17.0ms (0.6%)

simplify2.0ms (0.1%)

soundness196.0ms (6.7%)

end0.0ms (0%)

preprocess30.0ms (1%)

Profiling