Average Error: 0.0 → 0.0

Time: 1.7s

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 r8038 = re;
        double r8039 = im;
        double r8040 = r8038 * r8039;
        double r8041 = r8039 * r8038;
        double r8042 = r8040 + r8041;
        return r8042;
}

↓

double f(double re, double im) {
        double r8043 = re;
        double r8044 = im;
        double r8045 = r8044 + r8044;
        double r8046 = r8043 * r8045;
        return r8046;
}

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 2019196 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))