Average Error: 0.0 → 0.0
Time: 21.2s
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 r317632 = re;
        double r317633 = r317632 * r317632;
        double r317634 = im;
        double r317635 = r317634 * r317634;
        double r317636 = r317633 - r317635;
        return r317636;
}
↓
double f(double re, double im) {
        double r317637 = im;
        double r317638 = re;
        double r317639 = r317637 + r317638;
        double r317640 = r317638 - r317637;
        double r317641 = r317639 * r317640;
        return r317641;
}

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 2019168 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))