Average Error: 0.1 → 0.2
Time: 10.0s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{1}{6 \cdot \frac{1}{{x}^{2} - 3}}\]
\frac{x \cdot x - 3}{6}
↓
\frac{1}{6 \cdot \frac{1}{{x}^{2} - 3}}
double f(double x) {
        double r96279 = x;
        double r96280 = r96279 * r96279;
        double r96281 = 3.0;
        double r96282 = r96280 - r96281;
        double r96283 = 6.0;
        double r96284 = r96282 / r96283;
        return r96284;
}
↓
double f(double x) {
        double r96285 = 1.0;
        double r96286 = 6.0;
        double r96287 = x;
        double r96288 = 2.0;
        double r96289 = pow(r96287, r96288);
        double r96290 = 3.0;
        double r96291 = r96289 - r96290;
        double r96292 = r96285 / r96291;
        double r96293 = r96286 * r96292;
        double r96294 = r96285 / r96293;
        return r96294;
}

Error

Bits error versus x

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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 clear-num0.2

    \[\leadsto \color{blue}{\frac{1}{\frac{6}{x \cdot x - 3}}}\]
  4. Using strategy rm

  5. Applied div-inv0.2

    \[\leadsto \frac{1}{\color{blue}{6 \cdot \frac{1}{x \cdot x - 3}}}\]

  6. Simplified0.2

    \[\leadsto \frac{1}{6 \cdot \color{blue}{\frac{1}{{x}^{2} - 3}}}\]

  7. Final simplification0.2

    \[\leadsto \frac{1}{6 \cdot \frac{1}{{x}^{2} - 3}}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))