Average Error: 0.0 → 0.0
Time: 5.4s
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 r109112 = re;
        double r109113 = r109112 * r109112;
        double r109114 = im;
        double r109115 = r109114 * r109114;
        double r109116 = r109113 - r109115;
        return r109116;
}
↓
double f(double re, double im) {
        double r109117 = re;
        double r109118 = im;
        double r109119 = r109117 + r109118;
        double r109120 = r109117 - r109118;
        double r109121 = r109119 * r109120;
        return r109121;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))