Average Error: 0.0 → 0.0
Time: 20.0s
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 r591285 = re;
        double r591286 = r591285 * r591285;
        double r591287 = im;
        double r591288 = r591287 * r591287;
        double r591289 = r591286 - r591288;
        return r591289;
}
↓
double f(double re, double im) {
        double r591290 = re;
        double r591291 = im;
        double r591292 = r591290 + r591291;
        double r591293 = r591290 - r591291;
        double r591294 = r591292 * r591293;
        return r591294;
}

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 2019135 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))