Average Error: 0.1 → 0.0
Time: 2.6s
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 r211328 = x;
        double r211329 = r211328 * r211328;
        double r211330 = y;
        double r211331 = 4.0;
        double r211332 = r211330 * r211331;
        double r211333 = z;
        double r211334 = r211332 * r211333;
        double r211335 = r211329 - r211334;
        return r211335;
}
↓
double f(double x, double y, double z) {
        double r211336 = x;
        double r211337 = r211336 * r211336;
        double r211338 = y;
        double r211339 = 4.0;
        double r211340 = z;
        double r211341 = r211339 * r211340;
        double r211342 = r211338 * r211341;
        double r211343 = r211337 - r211342;
        return r211343;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))