Average Error: 0.0 → 0.0
Time: 2.8s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
double f(double x) {
        double r85781 = x;
        double r85782 = 2.30753;
        double r85783 = 0.27061;
        double r85784 = r85781 * r85783;
        double r85785 = r85782 + r85784;
        double r85786 = 1.0;
        double r85787 = 0.99229;
        double r85788 = 0.04481;
        double r85789 = r85781 * r85788;
        double r85790 = r85787 + r85789;
        double r85791 = r85790 * r85781;
        double r85792 = r85786 + r85791;
        double r85793 = r85785 / r85792;
        double r85794 = r85781 - r85793;
        return r85794;
}
↓
double f(double x) {
        double r85795 = x;
        double r85796 = 2.30753;
        double r85797 = 0.27061;
        double r85798 = r85795 * r85797;
        double r85799 = r85796 + r85798;
        double r85800 = 1.0;
        double r85801 = 1.0;
        double r85802 = 0.99229;
        double r85803 = 0.04481;
        double r85804 = r85795 * r85803;
        double r85805 = r85802 + r85804;
        double r85806 = r85805 * r85795;
        double r85807 = r85801 + r85806;
        double r85808 = r85800 / r85807;
        double r85809 = r85799 * r85808;
        double r85810 = r85795 - r85809;
        return r85810;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
  2. Using strategy rm

  3. Applied div-inv0.0

    \[\leadsto x - \color{blue}{\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}\]

  4. Final simplification0.0

    \[\leadsto x - \left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]

Reproduce

herbie shell --seed 2020024 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* (+ 0.99229 (* x 0.04481)) x)))))