Average Error: 0.0 → 0.0
Time: 3.1s
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 r68333 = re;
        double r68334 = im;
        double r68335 = r68333 * r68334;
        double r68336 = r68334 * r68333;
        double r68337 = r68335 + r68336;
        return r68337;
}
↓
double f(double re, double im) {
        double r68338 = re;
        double r68339 = im;
        double r68340 = r68339 + r68339;
        double r68341 = r68338 * r68340;
        return r68341;
}

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 2019152 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))