Average Error: 0.0 → 0.0
Time: 3.7s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[im \cdot \left(re + re\right)\]
re \cdot im + im \cdot re
↓
im \cdot \left(re + re\right)
double f(double re, double im) {
        double r190759 = re;
        double r190760 = im;
        double r190761 = r190759 * r190760;
        double r190762 = r190760 * r190759;
        double r190763 = r190761 + r190762;
        return r190763;
}
↓
double f(double re, double im) {
        double r190764 = im;
        double r190765 = re;
        double r190766 = r190765 + r190765;
        double r190767 = r190764 * r190766;
        return r190767;
}

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 *-commutative0.0

    \[\leadsto re \cdot im + \color{blue}{im \cdot re}\]

  5. Applied *-commutative0.0

    \[\leadsto \color{blue}{im \cdot re} + im \cdot re\]

  6. Applied distribute-lft-out0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))