Average Error: 31.5 → 0.0
Time: 441.0ms
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 r35092 = re;
        double r35093 = r35092 * r35092;
        double r35094 = im;
        double r35095 = r35094 * r35094;
        double r35096 = r35093 + r35095;
        double r35097 = sqrt(r35096);
        return r35097;
}
↓
double f(double re, double im) {
        double r35098 = re;
        double r35099 = im;
        double r35100 = hypot(r35098, r35099);
        return r35100;
}

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 31.5

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

  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 2019362 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))