Average Error: 0.0 → 0.0

Time: 4.7s

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 r8143 = re;
        double r8144 = r8143 * r8143;
        double r8145 = im;
        double r8146 = r8145 * r8145;
        double r8147 = r8144 - r8146;
        return r8147;
}

↓

double f(double re, double im) {
        double r8148 = re;
        double r8149 = r8148 * r8148;
        double r8150 = im;
        double r8151 = r8150 * r8150;
        double r8152 = r8149 - r8151;
        return r8152;
}

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 2019195 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))