Average Error: 0.0 → 0.0
Time: 9.9s
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 r386034 = re;
        double r386035 = r386034 * r386034;
        double r386036 = im;
        double r386037 = r386036 * r386036;
        double r386038 = r386035 - r386037;
        return r386038;
}
↓
double f(double re, double im) {
        double r386039 = re;
        double r386040 = r386039 * r386039;
        double r386041 = im;
        double r386042 = r386041 * r386041;
        double r386043 = r386040 - r386042;
        return r386043;
}

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)))