Average Error: 31.3 → 0.0
Time: 1.0s
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 r6143094 = re;
        double r6143095 = r6143094 * r6143094;
        double r6143096 = im;
        double r6143097 = r6143096 * r6143096;
        double r6143098 = r6143095 + r6143097;
        double r6143099 = sqrt(r6143098);
        return r6143099;
}
↓
double f(double re, double im) {
        double r6143100 = re;
        double r6143101 = im;
        double r6143102 = hypot(r6143100, r6143101);
        return r6143102;
}

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 31.3

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

  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 2019173 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))