math.abs on complex

Time bar (total: 1.5s)

analyze1.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
100%99.9%0%0.1%0%0%0%3
Compiler

Compiled 11 to 7 computations (36.4% saved)

sample1.2s (81%)

Results
1.2s8256×256valid
Bogosity

preprocess187.0ms (12.6%)

Algorithm
1×egg-herbie
Rules
104×fma-neg
90×fma-define
30×distribute-lft-neg-in
30×neg-sub0
28×unsub-neg
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1320-1(4.648892479263126e-298 1.3570352933035063e-159)(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
00-0-im
00-0-(*.f64 im im)
00-0-(*.f64 re re)
00-0-re
00-0-(+.f64 (*.f64 re re) (*.f64 im im))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02499
15199
29899
318599
428299
532199
633199
Stop Event
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
(sqrt.f64 (+.f64 (*.f64 (neg.f64 re) (neg.f64 re)) (*.f64 im im)))
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 (neg.f64 im) (neg.f64 im))))
(neg.f64 (sqrt.f64 (+.f64 (*.f64 (neg.f64 re) (neg.f64 re)) (*.f64 im im))))
(neg.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 (neg.f64 im) (neg.f64 im)))))
(sqrt.f64 (+.f64 (*.f64 im im) (*.f64 re re)))
Outputs
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
(hypot.f64 re im)
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
(hypot.f64 re im)
(sqrt.f64 (+.f64 (*.f64 (neg.f64 re) (neg.f64 re)) (*.f64 im im)))
(hypot.f64 re im)
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 (neg.f64 im) (neg.f64 im))))
(hypot.f64 re im)
(neg.f64 (sqrt.f64 (+.f64 (*.f64 (neg.f64 re) (neg.f64 re)) (*.f64 im im))))
(neg.f64 (hypot.f64 re im))
(neg.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 (neg.f64 im) (neg.f64 im)))))
(neg.f64 (hypot.f64 re im))
(sqrt.f64 (+.f64 (*.f64 im im) (*.f64 re re)))
(hypot.f64 re im)
Symmetry

(abs re)

(abs im)

(sort re im)

Compiler

Compiled 62 to 20 computations (67.7% saved)

eval0.0ms (0%)

Compiler

Compiled 5 to 3 computations (40% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(hypot.f64 re im)
Compiler

Compiled 5 to 3 computations (40% saved)

localize25.0ms (1.7%)

Compiler

Compiled 8 to 4 computations (50% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done000
Total011
Accuracy
100.0%
Counts
1 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(hypot.f64 re im)
Compiler

Compiled 18 to 10 computations (44.4% saved)

regimes17.0ms (1.1%)

Accuracy

Total -30.5b remaining (-∞%)

Threshold costs -30.5b (-∞%)

Counts
2 → 1
Calls
Call 1
Inputs
(hypot.f64 re im)
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
Outputs
(hypot.f64 re im)
Calls

6 calls:

4.0ms
im
3.0ms
re
2.0ms
(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
2.0ms
(+.f64 (*.f64 re re) (*.f64 im im))
2.0ms
(*.f64 im im)
Results
AccuracySegmentsBranch
100.0%1re
100.0%1im
100.0%1(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))
100.0%1(+.f64 (*.f64 re re) (*.f64 im im))
100.0%1(*.f64 re re)
100.0%1(*.f64 im im)
Compiler

Compiled 35 to 21 computations (40% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(hypot.f64 re im)
Outputs
(hypot.f64 re im)
Compiler

Compiled 5 to 3 computations (40% saved)

soundness22.0ms (1.5%)

Rules
104×fma-neg
90×fma-define
30×distribute-lft-neg-in
30×neg-sub0
28×unsub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02499
15199
29899
318599
428299
532199
633199
Stop Event
1×saturated
Compiler

Compiled 13 to 7 computations (46.2% saved)

end0.0ms (0%)

preprocess25.0ms (1.7%)

Remove

(sort re im)

(abs im)

(abs re)

Compiler

Compiled 90 to 54 computations (40% saved)

Profiling

Loading profile data...