Average Error: 31.9 → 0.0
Time: 848.0ms
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 r258 = re;
        double r259 = r258 * r258;
        double r260 = im;
        double r261 = r260 * r260;
        double r262 = r259 + r261;
        double r263 = sqrt(r262);
        return r263;
}
↓
double f(double re, double im) {
        double r264 = re;
        double r265 = im;
        double r266 = hypot(r264, r265);
        return r266;
}

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 31.9

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

  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 2020025 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))