Average Error: 0.0 → 0.0
Time: 7.6s
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 r447101 = re;
        double r447102 = r447101 * r447101;
        double r447103 = im;
        double r447104 = r447103 * r447103;
        double r447105 = r447102 - r447104;
        return r447105;
}
↓
double f(double re, double im) {
        double r447106 = im;
        double r447107 = re;
        double r447108 = r447106 + r447107;
        double r447109 = r447107 - r447106;
        double r447110 = r447108 * r447109;
        return r447110;
}

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 2019163 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))