Average Error: 0.0 → 0.0
Time: 1.9s
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 r8712 = re;
        double r8713 = r8712 * r8712;
        double r8714 = im;
        double r8715 = r8714 * r8714;
        double r8716 = r8713 - r8715;
        return r8716;
}
↓
double f(double re, double im) {
        double r8717 = re;
        double r8718 = im;
        double r8719 = r8717 + r8718;
        double r8720 = r8717 - r8718;
        double r8721 = r8719 * r8720;
        return r8721;
}

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 2019308 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))