Average Error: 0.0 → 0.0
Time: 12.3s
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 r325909 = re;
        double r325910 = r325909 * r325909;
        double r325911 = im;
        double r325912 = r325911 * r325911;
        double r325913 = r325910 - r325912;
        return r325913;
}
↓
double f(double re, double im) {
        double r325914 = im;
        double r325915 = re;
        double r325916 = r325914 + r325915;
        double r325917 = r325915 - r325914;
        double r325918 = r325916 * r325917;
        return r325918;
}

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 2019169 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))