Average Error: 0.0 → 0.0
Time: 17.7s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(re - im\right) \cdot \left(im + re\right)\]
re \cdot re - im \cdot im
↓
\left(re - im\right) \cdot \left(im + re\right)
double f(double re, double im) {
        double r366474 = re;
        double r366475 = r366474 * r366474;
        double r366476 = im;
        double r366477 = r366476 * r366476;
        double r366478 = r366475 - r366477;
        return r366478;
}
↓
double f(double re, double im) {
        double r366479 = re;
        double r366480 = im;
        double r366481 = r366479 - r366480;
        double r366482 = r366480 + r366479;
        double r366483 = r366481 * r366482;
        return r366483;
}

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

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

Reproduce

herbie shell --seed 2019168 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))