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 r8025 = re;
        double r8026 = im;
        double r8027 = r8025 * r8026;
        double r8028 = r8026 * r8025;
        double r8029 = r8027 + r8028;
        return r8029;
}

↓

double f(double re, double im) {
        double r8030 = re;
        double r8031 = im;
        double r8032 = r8031 + r8031;
        double r8033 = r8030 * r8032;
        return r8033;
}

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
\[\leadsto \color{blue}{re \cdot \left(im + im\right)}\]
Final simplification0.0
\[\leadsto re \cdot \left(im + im\right)\]

Reproduce

herbie shell --seed 2019179 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))