Average Error: 0.0 → 0.0
Time: 8.7s
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 r335445 = re;
        double r335446 = r335445 * r335445;
        double r335447 = im;
        double r335448 = r335447 * r335447;
        double r335449 = r335446 - r335448;
        return r335449;
}
↓
double f(double re, double im) {
        double r335450 = im;
        double r335451 = re;
        double r335452 = r335450 + r335451;
        double r335453 = r335451 - r335450;
        double r335454 = r335452 * r335453;
        return r335454;
}

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 2019151 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))