Average Error: 31.6 → 0.0
Time: 13.2s
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 r1632014 = re;
        double r1632015 = r1632014 * r1632014;
        double r1632016 = im;
        double r1632017 = r1632016 * r1632016;
        double r1632018 = r1632015 + r1632017;
        double r1632019 = sqrt(r1632018);
        return r1632019;
}
↓
double f(double re, double im) {
        double r1632020 = re;
        double r1632021 = im;
        double r1632022 = hypot(r1632020, r1632021);
        return r1632022;
}

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 31.6

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

  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))))