Average Error: 0.1 → 0.0
Time: 7.9s
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 r130753 = x;
        double r130754 = r130753 * r130753;
        double r130755 = y;
        double r130756 = 4.0;
        double r130757 = r130755 * r130756;
        double r130758 = z;
        double r130759 = r130757 * r130758;
        double r130760 = r130754 - r130759;
        return r130760;
}
↓
double f(double x, double y, double z) {
        double r130761 = x;
        double r130762 = r130761 * r130761;
        double r130763 = y;
        double r130764 = z;
        double r130765 = 4.0;
        double r130766 = r130764 * r130765;
        double r130767 = r130763 * r130766;
        double r130768 = r130762 - r130767;
        return r130768;
}

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)))