Average Error: 0.0 → 0.1
Time: 16.0s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \frac{\frac{1}{\frac{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}{2.30753 + x \cdot 0.27061000000000002}}}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \frac{\frac{1}{\frac{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}{2.30753 + x \cdot 0.27061000000000002}}}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}
double f(double x) {
        double r85396 = x;
        double r85397 = 2.30753;
        double r85398 = 0.27061;
        double r85399 = r85396 * r85398;
        double r85400 = r85397 + r85399;
        double r85401 = 1.0;
        double r85402 = 0.99229;
        double r85403 = 0.04481;
        double r85404 = r85396 * r85403;
        double r85405 = r85402 + r85404;
        double r85406 = r85405 * r85396;
        double r85407 = r85401 + r85406;
        double r85408 = r85400 / r85407;
        double r85409 = r85396 - r85408;
        return r85409;
}
↓
double f(double x) {
        double r85410 = x;
        double r85411 = 1.0;
        double r85412 = 1.0;
        double r85413 = 0.99229;
        double r85414 = 0.04481;
        double r85415 = r85410 * r85414;
        double r85416 = r85413 + r85415;
        double r85417 = r85416 * r85410;
        double r85418 = r85412 + r85417;
        double r85419 = sqrt(r85418);
        double r85420 = 2.30753;
        double r85421 = 0.27061;
        double r85422 = r85410 * r85421;
        double r85423 = r85420 + r85422;
        double r85424 = r85419 / r85423;
        double r85425 = r85411 / r85424;
        double r85426 = r85425 / r85419;
        double r85427 = r85410 - r85426;
        return r85427;
}

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. Using strategy rm

  6. Applied clear-num0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(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)))))