Average Error: 0.0 → 0.0
Time: 20.6s
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 r9865 = re;
        double r9866 = r9865 * r9865;
        double r9867 = im;
        double r9868 = r9867 * r9867;
        double r9869 = r9866 - r9868;
        return r9869;
}
↓
double f(double re, double im) {
        double r9870 = re;
        double r9871 = im;
        double r9872 = r9870 + r9871;
        double r9873 = r9870 - r9871;
        double r9874 = r9872 * r9873;
        return r9874;
}

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 2019304 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))