Average Error: 32.3 → 0.0
Time: 2.3s
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 r86144 = re;
        double r86145 = r86144 * r86144;
        double r86146 = im;
        double r86147 = r86146 * r86146;
        double r86148 = r86145 + r86147;
        double r86149 = sqrt(r86148);
        return r86149;
}
↓
double f(double re, double im) {
        double r86150 = re;
        double r86151 = im;
        double r86152 = hypot(r86150, r86151);
        return r86152;
}

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 32.3

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

  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 2020046 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))