Average Error: 0.0 → 0.0
Time: 12.7s
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 r68088 = x;
        double r68089 = 2.30753;
        double r68090 = 0.27061;
        double r68091 = r68088 * r68090;
        double r68092 = r68089 + r68091;
        double r68093 = 1.0;
        double r68094 = 0.99229;
        double r68095 = 0.04481;
        double r68096 = r68088 * r68095;
        double r68097 = r68094 + r68096;
        double r68098 = r68097 * r68088;
        double r68099 = r68093 + r68098;
        double r68100 = r68092 / r68099;
        double r68101 = r68088 - r68100;
        return r68101;
}
↓
double f(double x) {
        double r68102 = x;
        double r68103 = 2.30753;
        double r68104 = 0.27061;
        double r68105 = r68102 * r68104;
        double r68106 = r68103 + r68105;
        double r68107 = 1.0;
        double r68108 = 1.0;
        double r68109 = 0.99229;
        double r68110 = 0.04481;
        double r68111 = r68102 * r68110;
        double r68112 = r68109 + r68111;
        double r68113 = r68112 * r68102;
        double r68114 = r68108 + r68113;
        double r68115 = r68107 / r68114;
        double r68116 = r68106 * r68115;
        double r68117 = r68102 - r68116;
        return r68117;
}

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 2019208 
(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)))))