Average Error: 0.0 → 0.0
Time: 1.7s
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 r182 = re;
        double r183 = r182 * r182;
        double r184 = im;
        double r185 = r184 * r184;
        double r186 = r183 - r185;
        return r186;
}
↓
double f(double re, double im) {
        double r187 = re;
        double r188 = im;
        double r189 = r187 - r188;
        double r190 = r187 + r188;
        double r191 = r189 * r190;
        return r191;
}

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 2020045 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))