Average Error: 29.6 → 0.0
Time: 4.7s
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 r1348084 = re;
        double r1348085 = r1348084 * r1348084;
        double r1348086 = im;
        double r1348087 = r1348086 * r1348086;
        double r1348088 = r1348085 + r1348087;
        double r1348089 = sqrt(r1348088);
        return r1348089;
}
↓
double f(double re, double im) {
        double r1348090 = re;
        double r1348091 = im;
        double r1348092 = hypot(r1348090, r1348091);
        return r1348092;
}

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 29.6

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

  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 2019168 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))