Average Error: 0.0 → 0.1
Time: 1.7s
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 r154335 = x;
        double r154336 = r154335 * r154335;
        double r154337 = y;
        double r154338 = 4.0;
        double r154339 = r154337 * r154338;
        double r154340 = z;
        double r154341 = r154339 * r154340;
        double r154342 = r154336 - r154341;
        return r154342;
}
↓
double f(double x, double y, double z) {
        double r154343 = x;
        double r154344 = r154343 * r154343;
        double r154345 = y;
        double r154346 = 4.0;
        double r154347 = z;
        double r154348 = r154346 * r154347;
        double r154349 = r154345 * r154348;
        double r154350 = r154344 - r154349;
        return r154350;
}

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)))