Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(re + im\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(re + im\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r8768 = re;
        double r8769 = r8768 * r8768;
        double r8770 = im;
        double r8771 = r8770 * r8770;
        double r8772 = r8769 - r8771;
        return r8772;
}
↓
double f(double re, double im) {
        double r8773 = re;
        double r8774 = im;
        double r8775 = r8773 + r8774;
        double r8776 = r8773 - r8774;
        double r8777 = r8775 * r8776;
        return r8777;
}

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

    \[\leadsto \left(re + im\right) \cdot \left(re - im\right)\]

Reproduce

herbie shell --seed 2019322 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))