Average Error: 0.0 → 0.0
Time: 1.3s
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 r100195 = x;
        double r100196 = 2.30753;
        double r100197 = 0.27061;
        double r100198 = r100195 * r100197;
        double r100199 = r100196 + r100198;
        double r100200 = 1.0;
        double r100201 = 0.99229;
        double r100202 = 0.04481;
        double r100203 = r100195 * r100202;
        double r100204 = r100201 + r100203;
        double r100205 = r100204 * r100195;
        double r100206 = r100200 + r100205;
        double r100207 = r100199 / r100206;
        double r100208 = r100195 - r100207;
        return r100208;
}
↓
double f(double x) {
        double r100209 = x;
        double r100210 = 2.30753;
        double r100211 = 0.27061;
        double r100212 = r100209 * r100211;
        double r100213 = r100210 + r100212;
        double r100214 = 1.0;
        double r100215 = 0.99229;
        double r100216 = 0.04481;
        double r100217 = r100209 * r100216;
        double r100218 = r100215 + r100217;
        double r100219 = r100218 * r100209;
        double r100220 = r100214 + r100219;
        double r100221 = r100213 / r100220;
        double r100222 = r100209 - r100221;
        return r100222;
}

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 2020002 +o rules:numerics
(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)))))