Average Error: 0.0 → 0.0
Time: 3.5s
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 r99329 = x;
        double r99330 = 2.30753;
        double r99331 = 0.27061;
        double r99332 = r99329 * r99331;
        double r99333 = r99330 + r99332;
        double r99334 = 1.0;
        double r99335 = 0.99229;
        double r99336 = 0.04481;
        double r99337 = r99329 * r99336;
        double r99338 = r99335 + r99337;
        double r99339 = r99338 * r99329;
        double r99340 = r99334 + r99339;
        double r99341 = r99333 / r99340;
        double r99342 = r99329 - r99341;
        return r99342;
}
↓
double f(double x) {
        double r99343 = x;
        double r99344 = 1.0;
        double r99345 = 1.0;
        double r99346 = 0.99229;
        double r99347 = 0.04481;
        double r99348 = r99343 * r99347;
        double r99349 = r99346 + r99348;
        double r99350 = r99349 * r99343;
        double r99351 = r99345 + r99350;
        double r99352 = 2.30753;
        double r99353 = 0.27061;
        double r99354 = r99343 * r99353;
        double r99355 = r99352 + r99354;
        double r99356 = r99351 / r99355;
        double r99357 = r99344 / r99356;
        double r99358 = r99343 - r99357;
        return r99358;
}

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 2020035 
(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)))))