Average Error: 29.4 → 0.0
Time: 27.4s
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 r2065087 = re;
        double r2065088 = r2065087 * r2065087;
        double r2065089 = im;
        double r2065090 = r2065089 * r2065089;
        double r2065091 = r2065088 + r2065090;
        double r2065092 = sqrt(r2065091);
        return r2065092;
}
↓
double f(double re, double im) {
        double r2065093 = re;
        double r2065094 = im;
        double r2065095 = hypot(r2065093, r2065094);
        return r2065095;
}

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 29.4

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

  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 2019151 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))