Average Error: 0.0 → 0.0
Time: 15.2s
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 r8395 = re;
        double r8396 = r8395 * r8395;
        double r8397 = im;
        double r8398 = r8397 * r8397;
        double r8399 = r8396 - r8398;
        return r8399;
}
↓
double f(double re, double im) {
        double r8400 = re;
        double r8401 = im;
        double r8402 = r8400 - r8401;
        double r8403 = r8400 + r8401;
        double r8404 = r8402 * r8403;
        return r8404;
}

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 2019347 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))