Average Error: 0.0 → 0.0

Time: 1.8s

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 r9614 = re;
        double r9615 = r9614 * r9614;
        double r9616 = im;
        double r9617 = r9616 * r9616;
        double r9618 = r9615 - r9617;
        return r9618;
}

↓

double f(double re, double im) {
        double r9619 = re;
        double r9620 = r9619 * r9619;
        double r9621 = im;
        double r9622 = r9621 * r9621;
        double r9623 = r9620 - r9622;
        return r9623;
}

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 2019124 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))