Metrics for math.cube on complex, imaginary part

analyze15.0ms (1.1%)

Memory

4.4MiB live, 4.4MiB allocated

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 43 to 25 computations (41.9% saved)

sample1.2s (87.5%)

Memory: 11.6MiB live, 504.6MiB allocated
Precisions: Click to see Rival histograms. Total time spent on operations: 361.0ms
ival-mult: 261.0ms (72.3% of total)
ival-add: 60.0ms (16.6% of total)
ival-sub: 32.0ms (8.9% of total)
ival-true: 6.0ms (1.7% of total)
ival-assert: 3.0ms (0.8% of total)
Precisions: Click to see Base histograms. Total time spent on operations: 372.0ms
ival-mult: 271.0ms (72.9% of total)
ival-add: 60.0ms (16.1% of total)
ival-sub: 34.0ms (9.1% of total)
const: 6.0ms (1.6% of total)
Bogosity

preprocess127.0ms (9.1%)

Memory

6.0MiB live, 21.4MiB allocated

Algorithm

1×	egg-herbie

Rules

897×	`unsub-neg`
580×	`fma-define`
421×	`sub-neg`
400×	`distribute-lft-out`
384×	`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	4574	301
5	6808	301
6	7659	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.re (*.f64 x.im #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.re (*.f64 x.im #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.re (*.f64 x.im #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 (.f64 x.re x.re) (*.f64 x.im #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 (.f64 x.re x.re) (*.f64 x.im #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.re (*.f64 x.im #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%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0.1%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
	80.9%	(+.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)

simplify2.0ms (0.2%)

Memory

0.7MiB live, 0.7MiB allocated

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%)

Memory

0.4MiB live, 0.4MiB allocated

Stop Event

1×

fuel

Compiler

Compiled 21 to 10 computations (52.4% saved)

preprocess27.0ms (2%)

Memory

3.9MiB live, 35.5MiB allocated

Remove

(negabs x.im)

(abs x.re)

Compiler

Compiled 290 to 144 computations (50.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze15.0ms (1.1%)

sample1.2s (87.5%)

preprocess127.0ms (9.1%)

eval0.0ms (0%)

prune1.0ms (0.1%)

simplify2.0ms (0.2%)

soundness0.0ms (0%)

preprocess27.0ms (2%)

end0.0ms (0%)

Profiling