Average Error: 0.0 → 0.0
Time: 18.3s
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 r8659 = re;
        double r8660 = r8659 * r8659;
        double r8661 = im;
        double r8662 = r8661 * r8661;
        double r8663 = r8660 - r8662;
        return r8663;
}
↓
double f(double re, double im) {
        double r8664 = re;
        double r8665 = im;
        double r8666 = r8664 + r8665;
        double r8667 = r8664 - r8665;
        double r8668 = r8666 * r8667;
        return r8668;
}

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 2019326 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))