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 r8159 = re;
        double r8160 = im;
        double r8161 = r8159 * r8160;
        double r8162 = r8160 * r8159;
        double r8163 = r8161 + r8162;
        return r8163;
}

↓

double f(double re, double im) {
        double r8164 = re;
        double r8165 = im;
        double r8166 = r8165 + r8165;
        double r8167 = r8164 * r8166;
        return r8167;
}

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 2019326 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))