Average Error: 0.0 → 0.0
Time: 2.3s
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 r8562 = re;
        double r8563 = im;
        double r8564 = r8562 * r8563;
        double r8565 = r8563 * r8562;
        double r8566 = r8564 + r8565;
        return r8566;
}
↓
double f(double re, double im) {
        double r8567 = re;
        double r8568 = im;
        double r8569 = r8568 + r8568;
        double r8570 = r8567 * r8569;
        return r8570;
}

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 2019165 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))