Average Error: 0.2 → 0.1
Time: 21.5s
Precision: 64
\[\frac{x \cdot x - 3}{6}\]
↓
\[\left(0.1666666666666666574148081281236954964697 \cdot x\right) \cdot x - 0.5\]
\frac{x \cdot x - 3}{6}
↓
\left(0.1666666666666666574148081281236954964697 \cdot x\right) \cdot x - 0.5
double f(double x) {
        double r3643449 = x;
        double r3643450 = r3643449 * r3643449;
        double r3643451 = 3.0;
        double r3643452 = r3643450 - r3643451;
        double r3643453 = 6.0;
        double r3643454 = r3643452 / r3643453;
        return r3643454;
}
↓
double f(double x) {
        double r3643455 = 0.16666666666666666;
        double r3643456 = x;
        double r3643457 = r3643455 * r3643456;
        double r3643458 = r3643457 * r3643456;
        double r3643459 = 0.5;
        double r3643460 = r3643458 - r3643459;
        return r3643460;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  2. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{0.1666666666666666574148081281236954964697 \cdot {x}^{2} - 0.5}\]

  3. Simplified0.2

    \[\leadsto \color{blue}{0.1666666666666666574148081281236954964697 \cdot \left(x \cdot x\right) - 0.5}\]
  4. Using strategy rm

  5. Applied associate-*r*0.1

    \[\leadsto \color{blue}{\left(0.1666666666666666574148081281236954964697 \cdot x\right) \cdot x} - 0.5\]

  6. Final simplification0.1

    \[\leadsto \left(0.1666666666666666574148081281236954964697 \cdot x\right) \cdot x - 0.5\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H"
  (/ (- (* x x) 3.0) 6.0))