Average Error: 0.0 → 0.0
Time: 15.5s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(re - im\right) \cdot \left(re + im\right)\]
re \cdot re - im \cdot im
↓
\left(re - im\right) \cdot \left(re + im\right)
double f(double re, double im) {
        double r8169 = re;
        double r8170 = r8169 * r8169;
        double r8171 = im;
        double r8172 = r8171 * r8171;
        double r8173 = r8170 - r8172;
        return r8173;
}
↓
double f(double re, double im) {
        double r8174 = re;
        double r8175 = im;
        double r8176 = r8174 - r8175;
        double r8177 = r8174 + r8175;
        double r8178 = r8176 * r8177;
        return r8178;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\left(re - im\right) \cdot \left(re + im\right)}\]

  3. Final simplification0.0

    \[\leadsto \left(re - im\right) \cdot \left(re + im\right)\]

Reproduce

herbie shell --seed 2019326 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))