Average Error: 29.4 → 0.0
Time: 4.5s
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 r2046938 = re;
        double r2046939 = r2046938 * r2046938;
        double r2046940 = im;
        double r2046941 = r2046940 * r2046940;
        double r2046942 = r2046939 + r2046941;
        double r2046943 = sqrt(r2046942);
        return r2046943;
}
↓
double f(double re, double im) {
        double r2046944 = re;
        double r2046945 = im;
        double r2046946 = hypot(r2046944, r2046945);
        return r2046946;
}

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 29.4

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

  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 2019165 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))