Average Error: 0.0 → 0.0

Time: 1.3s

Precision: 64

\[re \cdot im + im \cdot re\]

↓

\[im \cdot \left(re + re\right)\]

re \cdot im + im \cdot re

↓

im \cdot \left(re + re\right)

double f(double re, double im) {
        double r8325 = re;
        double r8326 = im;
        double r8327 = r8325 * r8326;
        double r8328 = r8326 * r8325;
        double r8329 = r8327 + r8328;
        return r8329;
}

↓

double f(double re, double im) {
        double r8330 = im;
        double r8331 = re;
        double r8332 = r8331 + r8331;
        double r8333 = r8330 * r8332;
        return r8333;
}

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

Reproduce

herbie shell --seed 2019104 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))