Average Error: 0.0 → 0.0
Time: 5.5s
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 r176902 = re;
        double r176903 = im;
        double r176904 = r176902 * r176903;
        double r176905 = r176903 * r176902;
        double r176906 = r176904 + r176905;
        return r176906;
}
↓
double f(double re, double im) {
        double r176907 = re;
        double r176908 = im;
        double r176909 = r176908 + r176908;
        double r176910 = r176907 * r176909;
        return r176910;
}

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)))