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 r178939 = re;
        double r178940 = im;
        double r178941 = r178939 * r178940;
        double r178942 = r178940 * r178939;
        double r178943 = r178941 + r178942;
        return r178943;
}

↓

double f(double re, double im) {
        double r178944 = re;
        double r178945 = im;
        double r178946 = r178944 * r178945;
        double r178947 = r178946 + r178946;
        return r178947;
}

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 2019130 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))