Average Error: 0.0 → 0.0
Time: 926.0ms
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 r161 = re;
        double r162 = r161 * r161;
        double r163 = im;
        double r164 = r163 * r163;
        double r165 = r162 - r164;
        return r165;
}
↓
double f(double re, double im) {
        double r166 = re;
        double r167 = r166 * r166;
        double r168 = im;
        double r169 = r168 * r168;
        double r170 = r167 - r169;
        return r170;
}

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 2020065 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))