Average Error: 29.4 → 0.0
Time: 2.4s
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 r844956 = re;
        double r844957 = r844956 * r844956;
        double r844958 = im;
        double r844959 = r844958 * r844958;
        double r844960 = r844957 + r844959;
        double r844961 = sqrt(r844960);
        return r844961;
}
↓
double f(double re, double im) {
        double r844962 = re;
        double r844963 = im;
        double r844964 = hypot(r844962, r844963);
        return r844964;
}

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 2019132 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))