Average Error: 0.0 → 0.1
Time: 11.3s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}
double f(double x) {
        double r135320 = x;
        double r135321 = 2.30753;
        double r135322 = 0.27061;
        double r135323 = r135320 * r135322;
        double r135324 = r135321 + r135323;
        double r135325 = 1.0;
        double r135326 = 0.99229;
        double r135327 = 0.04481;
        double r135328 = r135320 * r135327;
        double r135329 = r135326 + r135328;
        double r135330 = r135329 * r135320;
        double r135331 = r135325 + r135330;
        double r135332 = r135324 / r135331;
        double r135333 = r135320 - r135332;
        return r135333;
}
↓
double f(double x) {
        double r135334 = x;
        double r135335 = 2.30753;
        double r135336 = 0.27061;
        double r135337 = r135334 * r135336;
        double r135338 = r135335 + r135337;
        double r135339 = 1.0;
        double r135340 = 0.99229;
        double r135341 = 0.04481;
        double r135342 = r135334 * r135341;
        double r135343 = r135340 + r135342;
        double r135344 = r135343 * r135334;
        double r135345 = r135339 + r135344;
        double r135346 = sqrt(r135345);
        double r135347 = r135338 / r135346;
        double r135348 = r135347 / r135346;
        double r135349 = r135334 - r135348;
        return r135349;
}

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 add-sqr-sqrt0.1

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

  4. Applied associate-/r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(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)))))