Average Error: 0.0 → 0.0
Time: 7.9s
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 r84089 = x;
        double r84090 = 2.30753;
        double r84091 = 0.27061;
        double r84092 = r84089 * r84091;
        double r84093 = r84090 + r84092;
        double r84094 = 1.0;
        double r84095 = 0.99229;
        double r84096 = 0.04481;
        double r84097 = r84089 * r84096;
        double r84098 = r84095 + r84097;
        double r84099 = r84098 * r84089;
        double r84100 = r84094 + r84099;
        double r84101 = r84093 / r84100;
        double r84102 = r84089 - r84101;
        return r84102;
}
↓
double f(double x) {
        double r84103 = x;
        double r84104 = 2.30753;
        double r84105 = 0.27061;
        double r84106 = r84103 * r84105;
        double r84107 = r84104 + r84106;
        double r84108 = 1.0;
        double r84109 = 1.0;
        double r84110 = 0.99229;
        double r84111 = 0.04481;
        double r84112 = r84103 * r84111;
        double r84113 = r84110 + r84112;
        double r84114 = r84113 * r84103;
        double r84115 = r84109 + r84114;
        double r84116 = r84108 / r84115;
        double r84117 = r84107 * r84116;
        double r84118 = r84103 - r84117;
        return r84118;
}

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 2020047 
(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)))))