Average Error: 32.3 → 0.0
Time: 3.1s
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 r107943 = re;
        double r107944 = r107943 * r107943;
        double r107945 = im;
        double r107946 = r107945 * r107945;
        double r107947 = r107944 + r107946;
        double r107948 = sqrt(r107947);
        return r107948;
}
↓
double f(double re, double im) {
        double r107949 = re;
        double r107950 = im;
        double r107951 = hypot(r107949, r107950);
        return r107951;
}

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 32.3

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

  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 2019344 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))