Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)}
double f(double x) {
        double r3941178 = x;
        double r3941179 = 2.30753;
        double r3941180 = 0.27061;
        double r3941181 = r3941178 * r3941180;
        double r3941182 = r3941179 + r3941181;
        double r3941183 = 1.0;
        double r3941184 = 0.99229;
        double r3941185 = 0.04481;
        double r3941186 = r3941178 * r3941185;
        double r3941187 = r3941184 + r3941186;
        double r3941188 = r3941187 * r3941178;
        double r3941189 = r3941183 + r3941188;
        double r3941190 = r3941182 / r3941189;
        double r3941191 = r3941178 - r3941190;
        return r3941191;
}
↓
double f(double x) {
        double r3941192 = x;
        double r3941193 = 2.30753;
        double r3941194 = 0.27061;
        double r3941195 = r3941192 * r3941194;
        double r3941196 = r3941193 + r3941195;
        double r3941197 = 1.0;
        double r3941198 = 1.0;
        double r3941199 = 0.04481;
        double r3941200 = r3941192 * r3941199;
        double r3941201 = 0.99229;
        double r3941202 = r3941200 + r3941201;
        double r3941203 = r3941192 * r3941202;
        double r3941204 = r3941198 + r3941203;
        double r3941205 = r3941197 / r3941204;
        double r3941206 = r3941196 * r3941205;
        double r3941207 = r3941192 - r3941206;
        return r3941207;
}

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 div-inv0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 
(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)))))