Average Error: 0.0 → 0.0
Time: 9.1s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(im + re\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r238754 = re;
        double r238755 = r238754 * r238754;
        double r238756 = im;
        double r238757 = r238756 * r238756;
        double r238758 = r238755 - r238757;
        return r238758;
}
↓
double f(double re, double im) {
        double r238759 = im;
        double r238760 = re;
        double r238761 = r238759 + r238760;
        double r238762 = r238760 - r238759;
        double r238763 = r238761 * r238762;
        return r238763;
}

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. Using strategy rm

  3. Applied difference-of-squares0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))