Average Error: 0.0 → 0.0
Time: 4.7s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(im + re\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r108925 = re;
        double r108926 = r108925 * r108925;
        double r108927 = im;
        double r108928 = r108927 * r108927;
        double r108929 = r108926 - r108928;
        return r108929;
}
↓
double f(double re, double im) {
        double r108930 = im;
        double r108931 = re;
        double r108932 = r108930 + r108931;
        double r108933 = r108931 - r108930;
        double r108934 = r108932 * r108933;
        return r108934;
}

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 0.0

    \[re \cdot re - im \cdot im\]
  2. Using strategy rm

  3. Applied difference-of-squares0.0

    \[\leadsto \color{blue}{\left(re + im\right) \cdot \left(re - im\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(im + re\right) \cdot \left(re - im\right)\]

Reproduce

herbie shell --seed 2019154 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))