Average Error: 0.0 → 0.0
Time: 1.1s
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 r145236 = x;
        double r145237 = r145236 * r145236;
        double r145238 = y;
        double r145239 = 4.0;
        double r145240 = r145238 * r145239;
        double r145241 = z;
        double r145242 = r145240 * r145241;
        double r145243 = r145237 - r145242;
        return r145243;
}
↓
double f(double x, double y, double z) {
        double r145244 = x;
        double r145245 = r145244 * r145244;
        double r145246 = y;
        double r145247 = 4.0;
        double r145248 = z;
        double r145249 = r145247 * r145248;
        double r145250 = r145246 * r145249;
        double r145251 = r145245 - r145250;
        return r145251;
}

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*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))