Average Error: 0.0 → 0.0
Time: 6.1s
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 r232180 = re;
        double r232181 = r232180 * r232180;
        double r232182 = im;
        double r232183 = r232182 * r232182;
        double r232184 = r232181 - r232183;
        return r232184;
}
↓
double f(double re, double im) {
        double r232185 = im;
        double r232186 = re;
        double r232187 = r232185 + r232186;
        double r232188 = r232186 - r232185;
        double r232189 = r232187 * r232188;
        return r232189;
}

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 2019192 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))