Metrics for math.cube on complex, imaginary 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 22 to 12 computations (45.5% saved)

sample3.0s (94.4%)

Results

570.0ms	8256×	0	valid-sollya
795.0ms	8256×	0	valid-rival

Bogosity

preprocess144.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

914×	`unsub-neg`
606×	`fma-define`
419×	`sub-neg`
392×	`distribute-lft-out`
383×	`distribute-lft-in`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	563
1	136	491
2	368	483
3	1517	309
4	4607	301
5	6832	301
6	7668	301

Stop Event

1×	node limit

Calls

Call 1

Inputs
(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
(+.f64 (.f64 (-.f64 (.f64 (neg.f64 x.re) (neg.f64 x.re)) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 (neg.f64 x.re) x.im) (.f64 x.im (neg.f64 x.re))) (neg.f64 x.re)))
(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 (neg.f64 x.im) (neg.f64 x.im))) (neg.f64 x.im)) (.f64 (+.f64 (.f64 x.re (neg.f64 x.im)) (.f64 (neg.f64 x.im) x.re)) x.re))
(neg.f64 (+.f64 (.f64 (-.f64 (.f64 (neg.f64 x.re) (neg.f64 x.re)) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 (neg.f64 x.re) x.im) (.f64 x.im (neg.f64 x.re))) (neg.f64 x.re))))
(neg.f64 (+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 (neg.f64 x.im) (neg.f64 x.im))) (neg.f64 x.im)) (.f64 (+.f64 (.f64 x.re (neg.f64 x.im)) (.f64 (neg.f64 x.im) x.re)) x.re)))
(+.f64 (.f64 (-.f64 (.f64 x.im x.im) (.f64 x.re x.re)) x.re) (.f64 (+.f64 (.f64 x.im x.re) (.f64 x.re x.im)) x.im))

Outputs
(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
(fma.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im (.f64 x.re (fma.f64 x.re x.im (.f64 x.re x.im))))
(fma.f64 x.re (.f64 #s(literal 2 binary64) (.f64 x.re x.im)) (.f64 x.im (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im))))
(fma.f64 x.re (.f64 x.re (.f64 x.im #s(literal 2 binary64))) (.f64 x.im (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im))))
(-.f64 (.f64 (.f64 x.re (*.f64 x.re x.im)) #s(literal 3 binary64)) (pow.f64 x.im #s(literal 3 binary64)))
(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re #s(literal 3 binary64)))) (pow.f64 x.im #s(literal 3 binary64)))
(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
(fma.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im (.f64 x.re (fma.f64 x.re x.im (.f64 x.re x.im))))
(fma.f64 x.re (.f64 #s(literal 2 binary64) (.f64 x.re x.im)) (.f64 x.im (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im))))
(fma.f64 x.re (.f64 x.re (.f64 x.im #s(literal 2 binary64))) (.f64 x.im (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im))))
(-.f64 (.f64 (.f64 x.re (*.f64 x.re x.im)) #s(literal 3 binary64)) (pow.f64 x.im #s(literal 3 binary64)))
(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re #s(literal 3 binary64)))) (pow.f64 x.im #s(literal 3 binary64)))
(+.f64 (.f64 (-.f64 (.f64 (neg.f64 x.re) (neg.f64 x.re)) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 (neg.f64 x.re) x.im) (.f64 x.im (neg.f64 x.re))) (neg.f64 x.re)))
(fma.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im (.f64 x.re (fma.f64 x.re x.im (.f64 x.re x.im))))
(fma.f64 x.re (.f64 #s(literal 2 binary64) (.f64 x.re x.im)) (.f64 x.im (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im))))
(fma.f64 x.re (.f64 x.re (.f64 x.im #s(literal 2 binary64))) (.f64 x.im (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im))))
(-.f64 (.f64 (.f64 x.re (*.f64 x.re x.im)) #s(literal 3 binary64)) (pow.f64 x.im #s(literal 3 binary64)))
(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re #s(literal 3 binary64)))) (pow.f64 x.im #s(literal 3 binary64)))
(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 (neg.f64 x.im) (neg.f64 x.im))) (neg.f64 x.im)) (.f64 (+.f64 (.f64 x.re (neg.f64 x.im)) (.f64 (neg.f64 x.im) x.re)) x.re))
(fma.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (neg.f64 x.im) (.f64 x.re (fma.f64 x.re (neg.f64 x.im) (.f64 x.re (neg.f64 x.im)))))
(fma.f64 x.re (.f64 #s(literal 2 binary64) (.f64 x.re (neg.f64 x.im))) (.f64 x.im (-.f64 (.f64 x.im x.im) (*.f64 x.re x.re))))
(fma.f64 x.im (-.f64 (.f64 x.im x.im) (.f64 x.re x.re)) (.f64 (.f64 x.re x.re) (*.f64 x.im #s(literal -2 binary64))))
(+.f64 (pow.f64 x.im #s(literal 3 binary64)) (.f64 (.f64 x.re (*.f64 x.re (neg.f64 x.im))) #s(literal 3 binary64)))
(-.f64 (pow.f64 x.im #s(literal 3 binary64)) (.f64 x.re (.f64 x.im (*.f64 x.re #s(literal 3 binary64)))))
(neg.f64 (+.f64 (.f64 (-.f64 (.f64 (neg.f64 x.re) (neg.f64 x.re)) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 (neg.f64 x.re) x.im) (.f64 x.im (neg.f64 x.re))) (neg.f64 x.re))))
(fma.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (neg.f64 x.im) (.f64 x.re (fma.f64 x.re (neg.f64 x.im) (.f64 x.re (neg.f64 x.im)))))
(fma.f64 x.re (.f64 #s(literal 2 binary64) (.f64 x.re (neg.f64 x.im))) (.f64 x.im (-.f64 (.f64 x.im x.im) (*.f64 x.re x.re))))
(fma.f64 x.im (-.f64 (.f64 x.im x.im) (.f64 x.re x.re)) (.f64 (.f64 x.re x.re) (*.f64 x.im #s(literal -2 binary64))))
(+.f64 (pow.f64 x.im #s(literal 3 binary64)) (.f64 (.f64 x.re (*.f64 x.re (neg.f64 x.im))) #s(literal 3 binary64)))
(-.f64 (pow.f64 x.im #s(literal 3 binary64)) (.f64 x.re (.f64 x.im (*.f64 x.re #s(literal 3 binary64)))))
(neg.f64 (+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 (neg.f64 x.im) (neg.f64 x.im))) (neg.f64 x.im)) (.f64 (+.f64 (.f64 x.re (neg.f64 x.im)) (.f64 (neg.f64 x.im) x.re)) x.re)))
(fma.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im (.f64 x.re (fma.f64 x.re x.im (.f64 x.re x.im))))
(fma.f64 x.re (.f64 #s(literal 2 binary64) (.f64 x.re x.im)) (.f64 x.im (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im))))
(fma.f64 x.re (.f64 x.re (.f64 x.im #s(literal 2 binary64))) (.f64 x.im (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im))))
(-.f64 (.f64 (.f64 x.re (*.f64 x.re x.im)) #s(literal 3 binary64)) (pow.f64 x.im #s(literal 3 binary64)))
(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re #s(literal 3 binary64)))) (pow.f64 x.im #s(literal 3 binary64)))
(+.f64 (.f64 (-.f64 (.f64 x.im x.im) (.f64 x.re x.re)) x.re) (.f64 (+.f64 (.f64 x.im x.re) (.f64 x.re x.im)) x.im))
(fma.f64 (-.f64 (.f64 x.im x.im) (.f64 x.re x.re)) x.re (.f64 x.im (fma.f64 x.re x.im (.f64 x.re x.im))))
(fma.f64 x.re (-.f64 (.f64 x.im x.im) (.f64 x.re x.re)) (.f64 x.im (.f64 #s(literal 2 binary64) (*.f64 x.re x.im))))
(fma.f64 x.re (-.f64 (.f64 x.im x.im) (.f64 x.re x.re)) (.f64 (.f64 x.im x.im) (*.f64 #s(literal 2 binary64) x.re)))
(-.f64 (.f64 (.f64 x.re (*.f64 x.im x.im)) #s(literal 3 binary64)) (pow.f64 x.re #s(literal 3 binary64)))
(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.im #s(literal 3 binary64)))) (pow.f64 x.re #s(literal 3 binary64)))

Symmetry

(abs x.re)

(negabs x.im)

Compiler

Compiled 21 to 11 computations (47.6% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
	80.3%	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Compiler

Compiled 42 to 22 computations (47.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative`
5×	`+-commutative`
3×	`sub-neg`
2×	`neg-sub0`
2×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	85
1	27	85
2	35	85
3	39	85
4	41	85

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Outputs

(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))

(+.f64 (*.f64 x.im (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))) (*.f64 x.re (+.f64 (*.f64 x.re x.im) (*.f64 x.re x.im))))

soundness0.0ms (0%)

Stop Event

1×

fuel

Compiler

Compiled 21 to 10 computations (52.4% saved)

preprocess30.0ms (0.9%)

Remove

(negabs x.im)

(abs x.re)

Compiler

Compiled 290 to 144 computations (50.3% saved)

math.cube on complex, imaginary part

analyze0.0ms (0%)

sample3.0s (94.4%)

preprocess144.0ms (4.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

soundness0.0ms (0%)

preprocess30.0ms (0.9%)

end0.0ms (0%)

Profiling