Average Error: 0.0 → 0.1
Time: 1.8s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot z\]
↓
\[x \cdot x - y \cdot \left(4 \cdot z\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot z
↓
x \cdot x - y \cdot \left(4 \cdot z\right)
double f(double x, double y, double z) {
        double r175428 = x;
        double r175429 = r175428 * r175428;
        double r175430 = y;
        double r175431 = 4.0;
        double r175432 = r175430 * r175431;
        double r175433 = z;
        double r175434 = r175432 * r175433;
        double r175435 = r175429 - r175434;
        return r175435;
}
↓
double f(double x, double y, double z) {
        double r175436 = x;
        double r175437 = r175436 * r175436;
        double r175438 = y;
        double r175439 = 4.0;
        double r175440 = z;
        double r175441 = r175439 * r175440;
        double r175442 = r175438 * r175441;
        double r175443 = r175437 - r175442;
        return r175443;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x \cdot x - \left(y \cdot 4\right) \cdot z\]
  2. Using strategy rm

  3. Applied associate-*l*0.1

    \[\leadsto x \cdot x - \color{blue}{y \cdot \left(4 \cdot z\right)}\]

  4. Final simplification0.1

    \[\leadsto x \cdot x - y \cdot \left(4 \cdot z\right)\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))