Average Error: 0.0 → 0.0
Time: 9.2s
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 r335367 = re;
        double r335368 = r335367 * r335367;
        double r335369 = im;
        double r335370 = r335369 * r335369;
        double r335371 = r335368 - r335370;
        return r335371;
}
↓
double f(double re, double im) {
        double r335372 = im;
        double r335373 = re;
        double r335374 = r335372 + r335373;
        double r335375 = r335373 - r335372;
        double r335376 = r335374 * r335375;
        return r335376;
}

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. Taylor expanded around inf 0.0

    \[\leadsto \color{blue}{{re}^{2} - {im}^{2}}\]

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019142 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))