Average Error: 0.0 → 0.0

Time: 2.5s

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 r9925 = re;
        double r9926 = r9925 * r9925;
        double r9927 = im;
        double r9928 = r9927 * r9927;
        double r9929 = r9926 - r9928;
        return r9929;
}

↓

double f(double re, double im) {
        double r9930 = re;
        double r9931 = r9930 * r9930;
        double r9932 = im;
        double r9933 = r9932 * r9932;
        double r9934 = r9931 - r9933;
        return r9934;
}

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 2019112 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))