Average Error: 0.0 → 0.0
Time: 12.5s
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 r332997 = re;
        double r332998 = r332997 * r332997;
        double r332999 = im;
        double r333000 = r332999 * r332999;
        double r333001 = r332998 - r333000;
        return r333001;
}
↓
double f(double re, double im) {
        double r333002 = im;
        double r333003 = re;
        double r333004 = r333002 + r333003;
        double r333005 = r333003 - r333002;
        double r333006 = r333004 * r333005;
        return r333006;
}

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 2019164 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))