Average Error: 0.0 → 0.0
Time: 1.7s
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 r8417 = re;
        double r8418 = im;
        double r8419 = r8417 * r8418;
        double r8420 = r8418 * r8417;
        double r8421 = r8419 + r8420;
        return r8421;
}
↓
double f(double re, double im) {
        double r8422 = re;
        double r8423 = im;
        double r8424 = r8423 + r8423;
        double r8425 = r8422 * r8424;
        return r8425;
}

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 2019162 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))