Average Error: 0.1 → 0.1
Time: 16.7s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x \cdot x + \left(-3\right)}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x \cdot x + \left(-3\right)}{6}
double f(double x) {
        double r38387 = x;
        double r38388 = r38387 * r38387;
        double r38389 = 3.0;
        double r38390 = r38388 - r38389;
        double r38391 = 6.0;
        double r38392 = r38390 / r38391;
        return r38392;
}
↓
double f(double x) {
        double r38393 = x;
        double r38394 = r38393 * r38393;
        double r38395 = 3.0;
        double r38396 = -r38395;
        double r38397 = r38394 + r38396;
        double r38398 = 6.0;
        double r38399 = r38397 / r38398;
        return r38399;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{x \cdot x - 3}{6}\]
  2. Using strategy rm

  3. Applied sub-neg0.1

    \[\leadsto \frac{\color{blue}{x \cdot x + \left(-3\right)}}{6}\]

  4. Final simplification0.1

    \[\leadsto \frac{x \cdot x + \left(-3\right)}{6}\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))