Average Error: 0.0 → 0.0

Time: 1.3s

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 r8237 = re;
        double r8238 = im;
        double r8239 = r8237 * r8238;
        double r8240 = r8238 * r8237;
        double r8241 = r8239 + r8240;
        return r8241;
}

↓

double f(double re, double im) {
        double r8242 = re;
        double r8243 = im;
        double r8244 = r8242 * r8243;
        double r8245 = r8244 + r8244;
        return r8245;
}

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
\[\leadsto \color{blue}{re \cdot im + re \cdot im}\]
Final simplification0.0
\[\leadsto re \cdot im + re \cdot im\]

Reproduce

herbie shell --seed 2019179 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))