Average Error: 0.0 → 0.0

Time: 4.9s

Precision: 64

\[re \cdot im + im \cdot re\]

↓

\[re \cdot im + re \cdot im\]

re \cdot im + im \cdot re

↓

re \cdot im + re \cdot im

double f(double re, double im) {
        double r131522 = re;
        double r131523 = im;
        double r131524 = r131522 * r131523;
        double r131525 = r131523 * r131522;
        double r131526 = r131524 + r131525;
        return r131526;
}

↓

double f(double re, double im) {
        double r131527 = re;
        double r131528 = im;
        double r131529 = r131527 * r131528;
        double r131530 = r131529 + r131529;
        return r131530;
}

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
\[re \cdot im + im \cdot re\]
Final simplification0.0
\[\leadsto re \cdot im + re \cdot im\]

Reproduce

herbie shell --seed 2019154 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))