Average Error: 0.0 → 0.0
Time: 1.3s
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 r8340 = re;
        double r8341 = im;
        double r8342 = r8340 * r8341;
        double r8343 = r8341 * r8340;
        double r8344 = r8342 + r8343;
        return r8344;
}
↓
double f(double re, double im) {
        double r8345 = re;
        double r8346 = im;
        double r8347 = r8346 + r8346;
        double r8348 = r8345 * r8347;
        return r8348;
}

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 2019142 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))