Average Error: 31.5 → 0.0
Time: 423.0ms
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 r42134 = re;
        double r42135 = r42134 * r42134;
        double r42136 = im;
        double r42137 = r42136 * r42136;
        double r42138 = r42135 + r42137;
        double r42139 = sqrt(r42138);
        return r42139;
}
↓
double f(double re, double im) {
        double r42140 = re;
        double r42141 = im;
        double r42142 = hypot(r42140, r42141);
        return r42142;
}

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 31.5

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

  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 2020021 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))