Average Error: 0.0 → 0.0
Time: 11.2s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
double f(double x) {
        double r84193 = x;
        double r84194 = 2.30753;
        double r84195 = 0.27061;
        double r84196 = r84193 * r84195;
        double r84197 = r84194 + r84196;
        double r84198 = 1.0;
        double r84199 = 0.99229;
        double r84200 = 0.04481;
        double r84201 = r84193 * r84200;
        double r84202 = r84199 + r84201;
        double r84203 = r84202 * r84193;
        double r84204 = r84198 + r84203;
        double r84205 = r84197 / r84204;
        double r84206 = r84193 - r84205;
        return r84206;
}
↓
double f(double x) {
        double r84207 = x;
        double r84208 = 2.30753;
        double r84209 = 0.27061;
        double r84210 = r84207 * r84209;
        double r84211 = r84208 + r84210;
        double r84212 = 1.0;
        double r84213 = 0.99229;
        double r84214 = 0.04481;
        double r84215 = r84207 * r84214;
        double r84216 = r84213 + r84215;
        double r84217 = r84216 * r84207;
        double r84218 = r84212 + r84217;
        double r84219 = r84211 / r84218;
        double r84220 = r84207 - r84219;
        return r84220;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019298 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061000000000002)) (+ 1 (* (+ 0.992290000000000005 (* x 0.044810000000000003)) x)))))