Average Error: 0.0 → 0.0
Time: 5.2s
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 r109117 = re;
        double r109118 = r109117 * r109117;
        double r109119 = im;
        double r109120 = r109119 * r109119;
        double r109121 = r109118 - r109120;
        return r109121;
}
↓
double f(double re, double im) {
        double r109122 = re;
        double r109123 = im;
        double r109124 = r109122 + r109123;
        double r109125 = r109122 - r109123;
        double r109126 = r109124 * r109125;
        return r109126;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))