Average Error: 0.0 → 0.0
Time: 7.7s
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 r322531 = re;
        double r322532 = r322531 * r322531;
        double r322533 = im;
        double r322534 = r322533 * r322533;
        double r322535 = r322532 - r322534;
        return r322535;
}
↓
double f(double re, double im) {
        double r322536 = im;
        double r322537 = re;
        double r322538 = r322536 + r322537;
        double r322539 = r322537 - r322536;
        double r322540 = r322538 * r322539;
        return r322540;
}

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 2019163 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))