Average Error: 31.6 → 0.0
Time: 608.0ms
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 r51014 = re;
        double r51015 = r51014 * r51014;
        double r51016 = im;
        double r51017 = r51016 * r51016;
        double r51018 = r51015 + r51017;
        double r51019 = sqrt(r51018);
        return r51019;
}
↓
double f(double re, double im) {
        double r51020 = re;
        double r51021 = im;
        double r51022 = hypot(r51020, r51021);
        return r51022;
}

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 31.6

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

  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 2019353 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))