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 r381678 = re;
        double r381679 = r381678 * r381678;
        double r381680 = im;
        double r381681 = r381680 * r381680;
        double r381682 = r381679 - r381681;
        return r381682;
}
↓
double f(double re, double im) {
        double r381683 = im;
        double r381684 = re;
        double r381685 = r381683 + r381684;
        double r381686 = r381684 - r381683;
        double r381687 = r381685 * r381686;
        return r381687;
}

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 0 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 2019141 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))