Average Error: 0.0 → 0.0

Time: 1.4s

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 r8323 = re;
        double r8324 = im;
        double r8325 = r8323 * r8324;
        double r8326 = r8324 * r8323;
        double r8327 = r8325 + r8326;
        return r8327;
}

↓

double f(double re, double im) {
        double r8328 = im;
        double r8329 = re;
        double r8330 = r8329 + r8329;
        double r8331 = r8328 * r8330;
        return r8331;
}

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 2019304 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))