Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \frac{1}{\frac{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}{2.30753 + x \cdot 0.27061000000000002}}\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \frac{1}{\frac{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}{2.30753 + x \cdot 0.27061000000000002}}
double f(double x) {
        double r106076 = x;
        double r106077 = 2.30753;
        double r106078 = 0.27061;
        double r106079 = r106076 * r106078;
        double r106080 = r106077 + r106079;
        double r106081 = 1.0;
        double r106082 = 0.99229;
        double r106083 = 0.04481;
        double r106084 = r106076 * r106083;
        double r106085 = r106082 + r106084;
        double r106086 = r106085 * r106076;
        double r106087 = r106081 + r106086;
        double r106088 = r106080 / r106087;
        double r106089 = r106076 - r106088;
        return r106089;
}
↓
double f(double x) {
        double r106090 = x;
        double r106091 = 1.0;
        double r106092 = 1.0;
        double r106093 = 0.99229;
        double r106094 = 0.04481;
        double r106095 = r106090 * r106094;
        double r106096 = r106093 + r106095;
        double r106097 = r106096 * r106090;
        double r106098 = r106092 + r106097;
        double r106099 = 2.30753;
        double r106100 = 0.27061;
        double r106101 = r106090 * r106100;
        double r106102 = r106099 + r106101;
        double r106103 = r106098 / r106102;
        double r106104 = r106091 / r106103;
        double r106105 = r106090 - r106104;
        return r106105;
}

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 clear-num0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020027 
(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)))))