Average Error: 31.5 → 0.0
Time: 590.0ms
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 r47840 = re;
        double r47841 = r47840 * r47840;
        double r47842 = im;
        double r47843 = r47842 * r47842;
        double r47844 = r47841 + r47843;
        double r47845 = sqrt(r47844);
        return r47845;
}
↓
double f(double re, double im) {
        double r47846 = re;
        double r47847 = im;
        double r47848 = hypot(r47846, r47847);
        return r47848;
}

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 2020024 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))