Average Error: 0.0 → 0.0
Time: 10.9s
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 r794000 = re;
        double r794001 = r794000 * r794000;
        double r794002 = im;
        double r794003 = r794002 * r794002;
        double r794004 = r794001 - r794003;
        return r794004;
}
↓
double f(double re, double im) {
        double r794005 = re;
        double r794006 = r794005 * r794005;
        double r794007 = im;
        double r794008 = r794007 * r794007;
        double r794009 = r794006 - r794008;
        return r794009;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[re \cdot re - im \cdot im\]

  2. Final simplification0.0

    \[\leadsto re \cdot re - im \cdot im\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))