Average Error: 0.0 → 0.0
Time: 7.8s
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 r253366 = re;
        double r253367 = r253366 * r253366;
        double r253368 = im;
        double r253369 = r253368 * r253368;
        double r253370 = r253367 - r253369;
        return r253370;
}
↓
double f(double re, double im) {
        double r253371 = re;
        double r253372 = im;
        double r253373 = r253371 + r253372;
        double r253374 = r253371 - r253372;
        double r253375 = r253373 * r253374;
        return r253375;
}

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 2019137 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))