Average Error: 0.0 → 0.0

Time: 1.5s

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 r8027 = re;
        double r8028 = im;
        double r8029 = r8027 * r8028;
        double r8030 = r8028 * r8027;
        double r8031 = r8029 + r8030;
        return r8031;
}

↓

double f(double re, double im) {
        double r8032 = re;
        double r8033 = im;
        double r8034 = r8033 + r8033;
        double r8035 = r8032 * r8034;
        return r8035;
}

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 2019174 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))