Average Error: 0.0 → 0.0

Time: 2.4s

Precision: 64

\[re \cdot re - im \cdot im\]

↓

\[re \cdot re - im \cdot im\]

re \cdot re - im \cdot im

↓

re \cdot re - im \cdot im

double f(double re, double im) {
        double r9914 = re;
        double r9915 = r9914 * r9914;
        double r9916 = im;
        double r9917 = r9916 * r9916;
        double r9918 = r9915 - r9917;
        return r9918;
}

↓

double f(double re, double im) {
        double r9919 = re;
        double r9920 = r9919 * r9919;
        double r9921 = im;
        double r9922 = r9921 * r9921;
        double r9923 = r9920 - r9922;
        return r9923;
}

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))