Average Error: 0.1 → 0.1
Time: 8.4s
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 r3195312 = x;
        double r3195313 = r3195312 * r3195312;
        double r3195314 = 3.0;
        double r3195315 = r3195313 - r3195314;
        double r3195316 = 6.0;
        double r3195317 = r3195315 / r3195316;
        return r3195317;
}
↓
double f(double x) {
        double r3195318 = x;
        double r3195319 = 6.0;
        double r3195320 = r3195318 / r3195319;
        double r3195321 = r3195318 * r3195320;
        double r3195322 = 3.0;
        double r3195323 = r3195322 / r3195319;
        double r3195324 = r3195321 - r3195323;
        return r3195324;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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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))