Average Error: 31.8 → 0.0
Time: 397.0ms
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 r38918 = re;
        double r38919 = r38918 * r38918;
        double r38920 = im;
        double r38921 = r38920 * r38920;
        double r38922 = r38919 + r38921;
        double r38923 = sqrt(r38922);
        return r38923;
}
↓
double f(double re, double im) {
        double r38924 = re;
        double r38925 = im;
        double r38926 = hypot(r38924, r38925);
        return r38926;
}

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 31.8

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

  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 2020036 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))