Average Error: 0.0 → 0.0

Time: 1.0s

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 r8152 = re;
        double r8153 = im;
        double r8154 = r8152 * r8153;
        double r8155 = r8153 * r8152;
        double r8156 = r8154 + r8155;
        return r8156;
}

↓

double f(double re, double im) {
        double r8157 = re;
        double r8158 = im;
        double r8159 = r8158 + r8158;
        double r8160 = r8157 * r8159;
        return r8160;
}

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