Average Error: 0.0 → 0.0
Time: 6.5s
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 r238818 = re;
        double r238819 = r238818 * r238818;
        double r238820 = im;
        double r238821 = r238820 * r238820;
        double r238822 = r238819 - r238821;
        return r238822;
}
↓
double f(double re, double im) {
        double r238823 = im;
        double r238824 = re;
        double r238825 = r238823 + r238824;
        double r238826 = r238824 - r238823;
        double r238827 = r238825 * r238826;
        return r238827;
}

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 2019171 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))