Average Error: 29.9 → 0.0
Time: 944.0ms
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 r682028 = re;
        double r682029 = r682028 * r682028;
        double r682030 = im;
        double r682031 = r682030 * r682030;
        double r682032 = r682029 + r682031;
        double r682033 = sqrt(r682032);
        return r682033;
}
↓
double f(double re, double im) {
        double r682034 = re;
        double r682035 = im;
        double r682036 = hypot(r682034, r682035);
        return r682036;
}

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 29.9

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

  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 2019153 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))