Average Error: 0.0 → 0.0

Time: 1.2s

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 r8042 = re;
        double r8043 = im;
        double r8044 = r8042 * r8043;
        double r8045 = r8043 * r8042;
        double r8046 = r8044 + r8045;
        return r8046;
}

↓

double f(double re, double im) {
        double r8047 = re;
        double r8048 = im;
        double r8049 = r8047 * r8048;
        double r8050 = r8049 + r8049;
        return r8050;
}

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 2019194 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))