Average Error: 0.0 → 0.0

Time: 6.9s

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 r9226 = re;
        double r9227 = r9226 * r9226;
        double r9228 = im;
        double r9229 = r9228 * r9228;
        double r9230 = r9227 - r9229;
        return r9230;
}

↓

double f(double re, double im) {
        double r9231 = re;
        double r9232 = r9231 * r9231;
        double r9233 = im;
        double r9234 = r9233 * r9233;
        double r9235 = r9232 - r9234;
        return r9235;
}

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 2019174 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))