Average Error: 0.1 → 0.1
Time: 12.2s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\frac{x}{6} \cdot x - \frac{3}{6}\]
\frac{x \cdot x - 3}{6}
↓
\frac{x}{6} \cdot x - \frac{3}{6}
double f(double x) {
        double r151509 = x;
        double r151510 = r151509 * r151509;
        double r151511 = 3.0;
        double r151512 = r151510 - r151511;
        double r151513 = 6.0;
        double r151514 = r151512 / r151513;
        return r151514;
}
↓
double f(double x) {
        double r151515 = x;
        double r151516 = 6.0;
        double r151517 = r151515 / r151516;
        double r151518 = r151517 * r151515;
        double r151519 = 3.0;
        double r151520 = r151519 / r151516;
        double r151521 = r151518 - r151520;
        return r151521;
}

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. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  :precision binary64
  (/ (- (* x x) 3) 6))