Average Error: 0.0 → 0.0
Time: 6.6s
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 r232169 = re;
        double r232170 = r232169 * r232169;
        double r232171 = im;
        double r232172 = r232171 * r232171;
        double r232173 = r232170 - r232172;
        return r232173;
}
↓
double f(double re, double im) {
        double r232174 = im;
        double r232175 = re;
        double r232176 = r232174 + r232175;
        double r232177 = r232175 - r232174;
        double r232178 = r232176 * r232177;
        return r232178;
}

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 2019165 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))