Average Error: 31.9 → 0.0
Time: 12.4s
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 r50080 = re;
        double r50081 = r50080 * r50080;
        double r50082 = im;
        double r50083 = r50082 * r50082;
        double r50084 = r50081 + r50083;
        double r50085 = sqrt(r50084);
        return r50085;
}
↓
double f(double re, double im) {
        double r50086 = re;
        double r50087 = im;
        double r50088 = hypot(r50086, r50087);
        return r50088;
}

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 2019304 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))