Average Error: 32.2 → 0.0
Time: 397.0ms
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 r106971 = re;
        double r106972 = r106971 * r106971;
        double r106973 = im;
        double r106974 = r106973 * r106973;
        double r106975 = r106972 + r106974;
        double r106976 = sqrt(r106975);
        return r106976;
}
↓
double f(double re, double im) {
        double r106977 = re;
        double r106978 = im;
        double r106979 = hypot(r106977, r106978);
        return r106979;
}

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))))