Average Error: 0.0 → 0.0
Time: 3.4s
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 r191843 = re;
        double r191844 = im;
        double r191845 = r191843 * r191844;
        double r191846 = r191844 * r191843;
        double r191847 = r191845 + r191846;
        return r191847;
}
↓
double f(double re, double im) {
        double r191848 = re;
        double r191849 = im;
        double r191850 = r191849 + r191849;
        double r191851 = r191848 * r191850;
        return r191851;
}

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

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

  4. Applied distribute-lft-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 2019165 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))