Average Error: 0.0 → 0.0
Time: 5.2s
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 r8057 = re;
        double r8058 = r8057 * r8057;
        double r8059 = im;
        double r8060 = r8059 * r8059;
        double r8061 = r8058 - r8060;
        return r8061;
}
↓
double f(double re, double im) {
        double r8062 = re;
        double r8063 = r8062 * r8062;
        double r8064 = im;
        double r8065 = r8064 * r8064;
        double r8066 = r8063 - r8065;
        return r8066;
}

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