Average Error: 0.0 → 0.0
Time: 3.6s
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 r198841 = re;
        double r198842 = im;
        double r198843 = r198841 * r198842;
        double r198844 = r198842 * r198841;
        double r198845 = r198843 + r198844;
        return r198845;
}
↓
double f(double re, double im) {
        double r198846 = re;
        double r198847 = im;
        double r198848 = r198847 + r198847;
        double r198849 = r198846 * r198848;
        return r198849;
}

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 2019171 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))