Average Error: 0.0 → 0.0

Time: 1.8s

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 r8309 = re;
        double r8310 = im;
        double r8311 = r8309 * r8310;
        double r8312 = r8310 * r8309;
        double r8313 = r8311 + r8312;
        return r8313;
}

↓

double f(double re, double im) {
        double r8314 = im;
        double r8315 = re;
        double r8316 = r8315 + r8315;
        double r8317 = r8314 * r8316;
        return r8317;
}

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 2019129 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))