Average Error: 31.3 → 0.0
Time: 409.0ms
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 r87940 = re;
        double r87941 = r87940 * r87940;
        double r87942 = im;
        double r87943 = r87942 * r87942;
        double r87944 = r87941 + r87943;
        double r87945 = sqrt(r87944);
        return r87945;
}
↓
double f(double re, double im) {
        double r87946 = re;
        double r87947 = im;
        double r87948 = hypot(r87946, r87947);
        return r87948;
}

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 31.3

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

  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 2020059 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))