Average Error: 0.0 → 0.0
Time: 1.8s
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 r85982 = x;
        double r85983 = 2.30753;
        double r85984 = 0.27061;
        double r85985 = r85982 * r85984;
        double r85986 = r85983 + r85985;
        double r85987 = 1.0;
        double r85988 = 0.99229;
        double r85989 = 0.04481;
        double r85990 = r85982 * r85989;
        double r85991 = r85988 + r85990;
        double r85992 = r85991 * r85982;
        double r85993 = r85987 + r85992;
        double r85994 = r85986 / r85993;
        double r85995 = r85982 - r85994;
        return r85995;
}
↓
double f(double x) {
        double r85996 = x;
        double r85997 = 2.30753;
        double r85998 = 0.27061;
        double r85999 = r85996 * r85998;
        double r86000 = r85997 + r85999;
        double r86001 = 1.0;
        double r86002 = 1.0;
        double r86003 = 0.99229;
        double r86004 = 0.04481;
        double r86005 = r85996 * r86004;
        double r86006 = r86003 + r86005;
        double r86007 = r86006 * r85996;
        double r86008 = r86002 + r86007;
        double r86009 = r86001 / r86008;
        double r86010 = r86000 * r86009;
        double r86011 = r85996 - r86010;
        return r86011;
}

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 2020062 
(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)))))