Average Error: 0.0 → 0.0

Time: 633.0ms

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 r8901 = re;
        double r8902 = im;
        double r8903 = r8901 * r8902;
        double r8904 = r8902 * r8901;
        double r8905 = r8903 + r8904;
        return r8905;
}

↓

double f(double re, double im) {
        double r8906 = im;
        double r8907 = re;
        double r8908 = r8907 + r8907;
        double r8909 = r8906 * r8908;
        return r8909;
}

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 2019322 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))