Average Error: 0.0 → 0.0
Time: 14.4s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(im + re\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r256509 = re;
        double r256510 = r256509 * r256509;
        double r256511 = im;
        double r256512 = r256511 * r256511;
        double r256513 = r256510 - r256512;
        return r256513;
}
↓
double f(double re, double im) {
        double r256514 = im;
        double r256515 = re;
        double r256516 = r256514 + r256515;
        double r256517 = r256515 - r256514;
        double r256518 = r256516 * r256517;
        return r256518;
}

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. Using strategy rm

  3. Applied difference-of-squares0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))