Average Error: 0.0 → 0.0
Time: 1.7s
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 r104700 = x;
        double r104701 = 2.30753;
        double r104702 = 0.27061;
        double r104703 = r104700 * r104702;
        double r104704 = r104701 + r104703;
        double r104705 = 1.0;
        double r104706 = 0.99229;
        double r104707 = 0.04481;
        double r104708 = r104700 * r104707;
        double r104709 = r104706 + r104708;
        double r104710 = r104709 * r104700;
        double r104711 = r104705 + r104710;
        double r104712 = r104704 / r104711;
        double r104713 = r104700 - r104712;
        return r104713;
}
↓
double f(double x) {
        double r104714 = x;
        double r104715 = 2.30753;
        double r104716 = 0.27061;
        double r104717 = r104714 * r104716;
        double r104718 = r104715 + r104717;
        double r104719 = 1.0;
        double r104720 = 1.0;
        double r104721 = 0.99229;
        double r104722 = 0.04481;
        double r104723 = r104714 * r104722;
        double r104724 = r104721 + r104723;
        double r104725 = r104724 * r104714;
        double r104726 = r104720 + r104725;
        double r104727 = r104719 / r104726;
        double r104728 = r104718 * r104727;
        double r104729 = r104714 - r104728;
        return r104729;
}

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 2020025 
(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)))))