Average Error: 0.1 → 0.1
Time: 2.0s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x \cdot x}{6} - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x \cdot x}{6} - \frac{3}{6}
double f(double x) {
        double r45207 = x;
        double r45208 = r45207 * r45207;
        double r45209 = 3.0;
        double r45210 = r45208 - r45209;
        double r45211 = 6.0;
        double r45212 = r45210 / r45211;
        return r45212;
}
↓
double f(double x) {
        double r45213 = x;
        double r45214 = r45213 * r45213;
        double r45215 = 6.0;
        double r45216 = r45214 / r45215;
        double r45217 = 3.0;
        double r45218 = r45217 / r45215;
        double r45219 = r45216 - r45218;
        return r45219;
}

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 div-sub0.1

    \[\leadsto \color{blue}{\frac{x \cdot x}{6} - \frac{3}{6}}\]

  4. Final simplification0.1

    \[\leadsto \frac{x \cdot x}{6} - \frac{3}{6}\]

Reproduce

herbie shell --seed 2019308 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))