Average Error: 31.0 → 0.0
Time: 1.4s
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 r56032 = re;
        double r56033 = r56032 * r56032;
        double r56034 = im;
        double r56035 = r56034 * r56034;
        double r56036 = r56033 + r56035;
        double r56037 = sqrt(r56036);
        return r56037;
}
↓
double f(double re, double im) {
        double r56038 = re;
        double r56039 = im;
        double r56040 = hypot(r56038, r56039);
        return r56040;
}

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 31.0

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

  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 2020001 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))