Average Error: 0.0 → 0.0

Time: 1.4s

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 r8423 = re;
        double r8424 = im;
        double r8425 = r8423 * r8424;
        double r8426 = r8424 * r8423;
        double r8427 = r8425 + r8426;
        return r8427;
}

↓

double f(double re, double im) {
        double r8428 = re;
        double r8429 = im;
        double r8430 = r8429 + r8429;
        double r8431 = r8428 * r8430;
        return r8431;
}

Error

The X axis uses an exponential scale — Bits error versus `re`

Try it out

In
Out

Enter valid numbers for all inputs

Derivation

Initial program 0.0
\[re \cdot im + im \cdot re\]
Simplified0.0
\[\leadsto \color{blue}{\left(im + im\right) \cdot re}\]
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)))