Average Error: 0.0 → 0.0
Time: 15.7s
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 r917062 = re;
        double r917063 = r917062 * r917062;
        double r917064 = im;
        double r917065 = r917064 * r917064;
        double r917066 = r917063 - r917065;
        return r917066;
}
↓
double f(double re, double im) {
        double r917067 = im;
        double r917068 = re;
        double r917069 = r917067 + r917068;
        double r917070 = r917068 - r917067;
        double r917071 = r917069 * r917070;
        return r917071;
}

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 2019138 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))