Average Error: 0.0 → 0.0

Time: 1.6s

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 r8282 = re;
        double r8283 = im;
        double r8284 = r8282 * r8283;
        double r8285 = r8283 * r8282;
        double r8286 = r8284 + r8285;
        return r8286;
}

↓

double f(double re, double im) {
        double r8287 = im;
        double r8288 = re;
        double r8289 = r8288 + r8288;
        double r8290 = r8287 * r8289;
        return r8290;
}

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 2019135 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))