Average Error: 0.0 → 0.1
Time: 804.0ms
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 r193442 = x;
        double r193443 = r193442 * r193442;
        double r193444 = y;
        double r193445 = 4.0;
        double r193446 = r193444 * r193445;
        double r193447 = z;
        double r193448 = r193446 * r193447;
        double r193449 = r193443 - r193448;
        return r193449;
}
↓
double f(double x, double y, double z) {
        double r193450 = x;
        double r193451 = r193450 * r193450;
        double r193452 = y;
        double r193453 = 4.0;
        double r193454 = z;
        double r193455 = r193453 * r193454;
        double r193456 = r193452 * r193455;
        double r193457 = r193451 - r193456;
        return r193457;
}

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 2019362 
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))