Average Error: 0.0 → 0.0
Time: 14.3s
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 r610777 = re;
        double r610778 = r610777 * r610777;
        double r610779 = im;
        double r610780 = r610779 * r610779;
        double r610781 = r610778 - r610780;
        return r610781;
}
↓
double f(double re, double im) {
        double r610782 = im;
        double r610783 = re;
        double r610784 = r610782 + r610783;
        double r610785 = r610783 - r610782;
        double r610786 = r610784 * r610785;
        return r610786;
}

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 2019135 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))