Average Error: 0.0 → 0.0
Time: 17.0s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
double f(double x) {
        double r77231 = x;
        double r77232 = 2.30753;
        double r77233 = 0.27061;
        double r77234 = r77231 * r77233;
        double r77235 = r77232 + r77234;
        double r77236 = 1.0;
        double r77237 = 0.99229;
        double r77238 = 0.04481;
        double r77239 = r77231 * r77238;
        double r77240 = r77237 + r77239;
        double r77241 = r77240 * r77231;
        double r77242 = r77236 + r77241;
        double r77243 = r77235 / r77242;
        double r77244 = r77231 - r77243;
        return r77244;
}
↓
double f(double x) {
        double r77245 = x;
        double r77246 = 2.30753;
        double r77247 = 0.27061;
        double r77248 = r77245 * r77247;
        double r77249 = r77246 + r77248;
        double r77250 = 1.0;
        double r77251 = 1.0;
        double r77252 = 0.99229;
        double r77253 = 0.04481;
        double r77254 = r77245 * r77253;
        double r77255 = r77252 + r77254;
        double r77256 = r77255 * r77245;
        double r77257 = r77251 + r77256;
        double r77258 = r77250 / r77257;
        double r77259 = r77249 * r77258;
        double r77260 = r77245 - r77259;
        return r77260;
}

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

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

Reproduce

herbie shell --seed 2019323 
(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)))))