Average Error: 0.0 → 0.0
Time: 10.3s
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 r317337 = re;
        double r317338 = r317337 * r317337;
        double r317339 = im;
        double r317340 = r317339 * r317339;
        double r317341 = r317338 - r317340;
        return r317341;
}
↓
double f(double re, double im) {
        double r317342 = im;
        double r317343 = re;
        double r317344 = r317342 + r317343;
        double r317345 = r317343 - r317342;
        double r317346 = r317344 * r317345;
        return r317346;
}

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 2019104 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))