Average Error: 29.7 → 0.0
Time: 1.2s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\mathsf{hypot}\left(re, im\right)\]
\sqrt{re \cdot re + im \cdot im}
↓
\mathsf{hypot}\left(re, im\right)
double f(double re, double im) {
        double r1034755 = re;
        double r1034756 = r1034755 * r1034755;
        double r1034757 = im;
        double r1034758 = r1034757 * r1034757;
        double r1034759 = r1034756 + r1034758;
        double r1034760 = sqrt(r1034759);
        return r1034760;
}
↓
double f(double re, double im) {
        double r1034761 = re;
        double r1034762 = im;
        double r1034763 = hypot(r1034761, r1034762);
        return r1034763;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.7

    \[\sqrt{re \cdot re + im \cdot im}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{hypot}\left(re, im\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{hypot}\left(re, im\right)\]

Reproduce

herbie shell --seed 2019146 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))