Average Error: 0.0 → 0.0

Time: 7.1s

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 r174799 = re;
        double r174800 = im;
        double r174801 = r174799 * r174800;
        double r174802 = r174800 * r174799;
        double r174803 = r174801 + r174802;
        return r174803;
}

↓

double f(double re, double im) {
        double r174804 = re;
        double r174805 = im;
        double r174806 = r174804 * r174805;
        double r174807 = r174806 + r174806;
        return r174807;
}

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 2019144 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))