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)

sample2.7s (84.3%)

Results

843.0ms	1047×	body	1024	infinite
578.0ms	1041×	body	1024	valid
517.0ms	2552×	body	256	valid
428.0ms	2571×	body	256	infinite
150.0ms	502×	body	512	valid
128.0ms	539×	body	512	infinite
3.0ms	4×	body	2048	valid

Bogosity

preprocess96.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1388×	`fma-def`
1228×	`distribute-lft-neg-in`
1086×	`fma-neg`
802×	`times-frac`
794×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	144
1	94	144
2	254	140
3	526	134
4	1151	132
5	3093	132
6	5261	132
7	7961	132

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify81.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1568×	`unswap-sqr`
1404×	`fma-def`
900×	`fabs-mul`
862×	`associate-/r*`
692×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	30	35
2	74	35
3	141	33
4	189	33
5	256	33
6	438	33
7	1104	33
8	3158	33
9	3540	33
10	4031	33
11	5670	33
12	6650	33

Stop Event

1×	node limit

Counts

1 → 4

Calls

Call 1

Inputs
(.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 (-.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) (.f64 1/2 (+.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))))

eval1.0ms (0%)

Compiler: Compiled 47 to 25 computations (46.8% saved)

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	4	1	5

Accurracy

100.0%

Counts

5 → 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)))
▶	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)

localize81.0ms (2.6%)

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 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 38 to 27 computations (28.9% saved)

regimes36.0ms (1.1%)

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:

23.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
2.0ms	(*.f64 1/2 (sin.f64 re))
2.0ms	(sin.f64 re)
2.0ms	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)

simplify4.0ms (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	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 (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)

soundness166.0ms (5.3%)

Rules

1568×	`unswap-sqr`
1404×	`fma-def`
900×	`fabs-mul`
862×	`associate-/r*`
692×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	30	35
2	74	35
3	141	33
4	189	33
5	256	33
6	438	33
7	1104	33
8	3158	33
9	3540	33
10	4031	33
11	5670	33
12	6650	33

Stop Event

1×	node limit

Compiler

Compiled 25 to 17 computations (32% saved)

end0.0ms (0%)

preprocess28.0ms (0.9%)

Remove: (abs im)
Compiler: Compiled 80 to 62 computations (22.5% saved)

analyze0.0ms (0%)

sample2.7s (84.3%)

preprocess96.0ms (3.1%)

simplify81.0ms (2.6%)

eval1.0ms (0%)

prune2.0ms (0%)

localize81.0ms (2.6%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes36.0ms (1.1%)

simplify4.0ms (0.1%)

soundness166.0ms (5.3%)

end0.0ms (0%)

preprocess28.0ms (0.9%)

Profiling