Average Error: 0.0 → 0.0
Time: 10.1s
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 r187 = re;
        double r188 = r187 * r187;
        double r189 = im;
        double r190 = r189 * r189;
        double r191 = r188 - r190;
        return r191;
}
↓
double f(double re, double im) {
        double r192 = re;
        double r193 = im;
        double r194 = r192 - r193;
        double r195 = r192 + r193;
        double r196 = r194 * r195;
        return r196;
}

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 2019350 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))