Average Error: 0.0 → 0.1
Time: 11.4s
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 r135319 = x;
        double r135320 = 2.30753;
        double r135321 = 0.27061;
        double r135322 = r135319 * r135321;
        double r135323 = r135320 + r135322;
        double r135324 = 1.0;
        double r135325 = 0.99229;
        double r135326 = 0.04481;
        double r135327 = r135319 * r135326;
        double r135328 = r135325 + r135327;
        double r135329 = r135328 * r135319;
        double r135330 = r135324 + r135329;
        double r135331 = r135323 / r135330;
        double r135332 = r135319 - r135331;
        return r135332;
}
↓
double f(double x) {
        double r135333 = x;
        double r135334 = 2.30753;
        double r135335 = 0.27061;
        double r135336 = r135333 * r135335;
        double r135337 = r135334 + r135336;
        double r135338 = 1.0;
        double r135339 = 0.99229;
        double r135340 = 0.04481;
        double r135341 = r135333 * r135340;
        double r135342 = r135339 + r135341;
        double r135343 = r135342 * r135333;
        double r135344 = r135338 + r135343;
        double r135345 = sqrt(r135344);
        double r135346 = r135337 / r135345;
        double r135347 = r135346 / r135345;
        double r135348 = r135333 - r135347;
        return r135348;
}

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)))))