Average Error: 0.1 → 0.1
Time: 9.7s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[x \cdot \frac{x}{6} - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
x \cdot \frac{x}{6} - \frac{3}{6}
double f(double x) {
        double r3292302 = x;
        double r3292303 = r3292302 * r3292302;
        double r3292304 = 3.0;
        double r3292305 = r3292303 - r3292304;
        double r3292306 = 6.0;
        double r3292307 = r3292305 / r3292306;
        return r3292307;
}
↓
double f(double x) {
        double r3292308 = x;
        double r3292309 = 6.0;
        double r3292310 = r3292308 / r3292309;
        double r3292311 = r3292308 * r3292310;
        double r3292312 = 3.0;
        double r3292313 = r3292312 / r3292309;
        double r3292314 = r3292311 - r3292313;
        return r3292314;
}

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 div-sub0.1

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

  5. Applied *-un-lft-identity0.1

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

  6. Applied times-frac0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  (/ (- (* x x) 3.0) 6.0))