Average Error: 0.0 → 0.0
Time: 21.0s
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 r554363 = re;
        double r554364 = r554363 * r554363;
        double r554365 = im;
        double r554366 = r554365 * r554365;
        double r554367 = r554364 - r554366;
        return r554367;
}
↓
double f(double re, double im) {
        double r554368 = im;
        double r554369 = re;
        double r554370 = r554368 + r554369;
        double r554371 = r554369 - r554368;
        double r554372 = r554370 * r554371;
        return r554372;
}

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 2019143 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))