Average Error: 0.1 → 0.0
Time: 8.8s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot z\]
↓
\[x \cdot x - y \cdot \left(z \cdot 4\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot z
↓
x \cdot x - y \cdot \left(z \cdot 4\right)
double f(double x, double y, double z) {
        double r198249 = x;
        double r198250 = r198249 * r198249;
        double r198251 = y;
        double r198252 = 4.0;
        double r198253 = r198251 * r198252;
        double r198254 = z;
        double r198255 = r198253 * r198254;
        double r198256 = r198250 - r198255;
        return r198256;
}
↓
double f(double x, double y, double z) {
        double r198257 = x;
        double r198258 = r198257 * r198257;
        double r198259 = y;
        double r198260 = z;
        double r198261 = 4.0;
        double r198262 = r198260 * r198261;
        double r198263 = r198259 * r198262;
        double r198264 = r198258 - r198263;
        return r198264;
}

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 0.1

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

  3. Applied associate-*l*0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))