Average Error: 0.0 → 0.0

Time: 4.6s

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 r8049 = re;
        double r8050 = r8049 * r8049;
        double r8051 = im;
        double r8052 = r8051 * r8051;
        double r8053 = r8050 - r8052;
        return r8053;
}

↓

double f(double re, double im) {
        double r8054 = re;
        double r8055 = r8054 * r8054;
        double r8056 = im;
        double r8057 = r8056 * r8056;
        double r8058 = r8055 - r8057;
        return r8058;
}

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 2019196 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))