Average Error: 29.4 → 0.0
Time: 1.6s
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 r811975 = re;
        double r811976 = r811975 * r811975;
        double r811977 = im;
        double r811978 = r811977 * r811977;
        double r811979 = r811976 + r811978;
        double r811980 = sqrt(r811979);
        return r811980;
}
↓
double f(double re, double im) {
        double r811981 = re;
        double r811982 = im;
        double r811983 = hypot(r811981, r811982);
        return r811983;
}

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 2019130 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))