Average Error: 0.0 → 0.0

Time: 1.1s

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 r8316 = re;
        double r8317 = im;
        double r8318 = r8316 * r8317;
        double r8319 = r8317 * r8316;
        double r8320 = r8318 + r8319;
        return r8320;
}

↓

double f(double re, double im) {
        double r8321 = im;
        double r8322 = re;
        double r8323 = r8322 + r8322;
        double r8324 = r8321 * r8323;
        return r8324;
}

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 2019107 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))