Average Error: 0.0 → 0.0
Time: 6.6s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[re \cdot \left(im + im\right)\]
re \cdot im + im \cdot re
↓
re \cdot \left(im + im\right)
double f(double re, double im) {
        double r231839 = re;
        double r231840 = im;
        double r231841 = r231839 * r231840;
        double r231842 = r231840 * r231839;
        double r231843 = r231841 + r231842;
        return r231843;
}
↓
double f(double re, double im) {
        double r231844 = re;
        double r231845 = im;
        double r231846 = r231845 + r231845;
        double r231847 = r231844 * r231846;
        return r231847;
}

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

    \[re \cdot im + im \cdot re\]

  2. Simplified0.0

    \[\leadsto \color{blue}{im \cdot re + im \cdot re}\]
  3. Using strategy rm

  4. Applied distribute-rgt-out0.0

    \[\leadsto \color{blue}{re \cdot \left(im + im\right)}\]

  5. Final simplification0.0

    \[\leadsto re \cdot \left(im + im\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))