Average Error: 29.4 → 0.0
Time: 10.1s
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 r1051172 = re;
        double r1051173 = r1051172 * r1051172;
        double r1051174 = im;
        double r1051175 = r1051174 * r1051174;
        double r1051176 = r1051173 + r1051175;
        double r1051177 = sqrt(r1051176);
        return r1051177;
}
↓
double f(double re, double im) {
        double r1051178 = re;
        double r1051179 = im;
        double r1051180 = hypot(r1051178, r1051179);
        return r1051180;
}

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))))