Average Error: 0.0 → 0.0
Time: 19.5s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(re - im\right) \cdot \left(re + im\right)\]
re \cdot re - im \cdot im
↓
\left(re - im\right) \cdot \left(re + im\right)
double f(double re, double im) {
        double r335817 = re;
        double r335818 = r335817 * r335817;
        double r335819 = im;
        double r335820 = r335819 * r335819;
        double r335821 = r335818 - r335820;
        return r335821;
}
↓
double f(double re, double im) {
        double r335822 = re;
        double r335823 = im;
        double r335824 = r335822 - r335823;
        double r335825 = r335822 + r335823;
        double r335826 = r335824 * r335825;
        return r335826;
}

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

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))