Average Error: 30.9 → 0.0
Time: 5.2s
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 r39813 = re;
        double r39814 = r39813 * r39813;
        double r39815 = im;
        double r39816 = r39815 * r39815;
        double r39817 = r39814 + r39816;
        double r39818 = sqrt(r39817);
        return r39818;
}
↓
double f(double re, double im) {
        double r39819 = re;
        double r39820 = im;
        double r39821 = hypot(r39819, r39820);
        return r39821;
}

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 30.9

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

  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 2019194 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))