Average Error: 0.0 → 0.0
Time: 17.6s
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 r8632 = re;
        double r8633 = r8632 * r8632;
        double r8634 = im;
        double r8635 = r8634 * r8634;
        double r8636 = r8633 - r8635;
        return r8636;
}
↓
double f(double re, double im) {
        double r8637 = re;
        double r8638 = im;
        double r8639 = r8637 + r8638;
        double r8640 = r8637 - r8638;
        double r8641 = r8639 * r8640;
        return r8641;
}

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 2019303 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))