Average Error: 0.0 → 0.0
Time: 11.7s
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 r514184 = re;
        double r514185 = r514184 * r514184;
        double r514186 = im;
        double r514187 = r514186 * r514186;
        double r514188 = r514185 - r514187;
        return r514188;
}
↓
double f(double re, double im) {
        double r514189 = im;
        double r514190 = re;
        double r514191 = r514189 + r514190;
        double r514192 = r514190 - r514189;
        double r514193 = r514191 * r514192;
        return r514193;
}

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 2019179 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))