Average Error: 0.0 → 0.0
Time: 5.0s
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 r203746 = re;
        double r203747 = im;
        double r203748 = r203746 * r203747;
        double r203749 = r203747 * r203746;
        double r203750 = r203748 + r203749;
        return r203750;
}
↓
double f(double re, double im) {
        double r203751 = re;
        double r203752 = im;
        double r203753 = r203752 + r203752;
        double r203754 = r203751 * r203753;
        return r203754;
}

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 2019163 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))