Average Error: 0.0 → 0.0
Time: 10.4s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \frac{1}{\frac{x \cdot \left(0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot x\right) + 1}{2.307529999999999859028321225196123123169 + 0.2706100000000000171951342053944244980812 \cdot x}}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \frac{1}{\frac{x \cdot \left(0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot x\right) + 1}{2.307529999999999859028321225196123123169 + 0.2706100000000000171951342053944244980812 \cdot x}}
double f(double x) {
        double r78190 = x;
        double r78191 = 2.30753;
        double r78192 = 0.27061;
        double r78193 = r78190 * r78192;
        double r78194 = r78191 + r78193;
        double r78195 = 1.0;
        double r78196 = 0.99229;
        double r78197 = 0.04481;
        double r78198 = r78190 * r78197;
        double r78199 = r78196 + r78198;
        double r78200 = r78199 * r78190;
        double r78201 = r78195 + r78200;
        double r78202 = r78194 / r78201;
        double r78203 = r78190 - r78202;
        return r78203;
}
↓
double f(double x) {
        double r78204 = x;
        double r78205 = 1.0;
        double r78206 = 0.99229;
        double r78207 = 0.04481;
        double r78208 = r78207 * r78204;
        double r78209 = r78206 + r78208;
        double r78210 = r78204 * r78209;
        double r78211 = 1.0;
        double r78212 = r78210 + r78211;
        double r78213 = 2.30753;
        double r78214 = 0.27061;
        double r78215 = r78214 * r78204;
        double r78216 = r78213 + r78215;
        double r78217 = r78212 / r78216;
        double r78218 = r78205 / r78217;
        double r78219 = r78204 - r78218;
        return r78219;
}

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

    \[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
  2. Using strategy rm

  3. Applied clear-num0.0

    \[\leadsto x - \color{blue}{\frac{1}{\frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}}\]

  4. Simplified0.0

    \[\leadsto x - \frac{1}{\color{blue}{\frac{1 + x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)}{0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169}}}\]

  5. Final simplification0.0

    \[\leadsto x - \frac{1}{\frac{x \cdot \left(0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot x\right) + 1}{2.307529999999999859028321225196123123169 + 0.2706100000000000171951342053944244980812 \cdot x}}\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))