Average Error: 0.0 → 0.0
Time: 1.2s
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 r8441 = re;
        double r8442 = im;
        double r8443 = r8441 * r8442;
        double r8444 = r8442 * r8441;
        double r8445 = r8443 + r8444;
        return r8445;
}
↓
double f(double re, double im) {
        double r8446 = re;
        double r8447 = im;
        double r8448 = r8447 + r8447;
        double r8449 = r8446 * r8448;
        return r8449;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019119 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))