Average Error: 0.0 → 0.0
Time: 11.6s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(im + re\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r9635 = re;
        double r9636 = r9635 * r9635;
        double r9637 = im;
        double r9638 = r9637 * r9637;
        double r9639 = r9636 - r9638;
        return r9639;
}
↓
double f(double re, double im) {
        double r9640 = im;
        double r9641 = re;
        double r9642 = r9640 + r9641;
        double r9643 = r9641 - r9640;
        double r9644 = r9642 * r9643;
        return r9644;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\left(im + re\right) \cdot \left(re - im\right)}\]

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))