Average Error: 0.0 → 0.0
Time: 9.5s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
double f(double x) {
        double r52853 = 0.70711;
        double r52854 = 2.30753;
        double r52855 = x;
        double r52856 = 0.27061;
        double r52857 = r52855 * r52856;
        double r52858 = r52854 + r52857;
        double r52859 = 1.0;
        double r52860 = 0.99229;
        double r52861 = 0.04481;
        double r52862 = r52855 * r52861;
        double r52863 = r52860 + r52862;
        double r52864 = r52855 * r52863;
        double r52865 = r52859 + r52864;
        double r52866 = r52858 / r52865;
        double r52867 = r52866 - r52855;
        double r52868 = r52853 * r52867;
        return r52868;
}
↓
double f(double x) {
        double r52869 = 0.70711;
        double r52870 = 2.30753;
        double r52871 = x;
        double r52872 = 0.27061;
        double r52873 = r52871 * r52872;
        double r52874 = r52870 + r52873;
        double r52875 = 1.0;
        double r52876 = 0.99229;
        double r52877 = 0.04481;
        double r52878 = r52871 * r52877;
        double r52879 = r52876 + r52878;
        double r52880 = r52871 * r52879;
        double r52881 = r52875 + r52880;
        double r52882 = r52874 / r52881;
        double r52883 = r52882 - r52871;
        double r52884 = r52869 * r52883;
        return r52884;
}

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

    \[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]

  2. Final simplification0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]

Reproduce

herbie shell --seed 2019297 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.707110000000000016 (- (/ (+ 2.30753 (* x 0.27061000000000002)) (+ 1 (* x (+ 0.992290000000000005 (* x 0.044810000000000003))))) x)))