Average Error: 32.2 → 0.0
Time: 430.0ms
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 r92196 = re;
        double r92197 = r92196 * r92196;
        double r92198 = im;
        double r92199 = r92198 * r92198;
        double r92200 = r92197 + r92199;
        double r92201 = sqrt(r92200);
        return r92201;
}
↓
double f(double re, double im) {
        double r92202 = re;
        double r92203 = im;
        double r92204 = hypot(r92202, r92203);
        return r92204;
}

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 32.2

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

  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 2020047 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))