Average Error: 31.0 → 0.0
Time: 9.1s
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 r48943 = re;
        double r48944 = r48943 * r48943;
        double r48945 = im;
        double r48946 = r48945 * r48945;
        double r48947 = r48944 + r48946;
        double r48948 = sqrt(r48947);
        return r48948;
}
↓
double f(double re, double im) {
        double r48949 = re;
        double r48950 = im;
        double r48951 = hypot(r48949, r48950);
        return r48951;
}

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 31.0

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

  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 2020045 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))