Average Error: 0.0 → 0
Time: 24.1s
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 r180884 = re;
        double r180885 = im;
        double r180886 = r180884 * r180885;
        double r180887 = r180885 * r180884;
        double r180888 = r180886 + r180887;
        return r180888;
}
↓
double f(double re, double im) {
        double r180889 = re;
        double r180890 = im;
        double r180891 = r180890 + r180890;
        double r180892 = r180889 * r180891;
        return r180892;
}

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

    \[\leadsto \color{blue}{im \cdot re + im \cdot re}\]
  3. Using strategy rm

  4. Applied distribute-rgt-out0

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

  5. Final simplification0

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

Reproduce

herbie shell --seed 2019200 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))