Average Error: 0.0 → 0.0
Time: 2.5s
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 r81827 = 0.70711;
        double r81828 = 2.30753;
        double r81829 = x;
        double r81830 = 0.27061;
        double r81831 = r81829 * r81830;
        double r81832 = r81828 + r81831;
        double r81833 = 1.0;
        double r81834 = 0.99229;
        double r81835 = 0.04481;
        double r81836 = r81829 * r81835;
        double r81837 = r81834 + r81836;
        double r81838 = r81829 * r81837;
        double r81839 = r81833 + r81838;
        double r81840 = r81832 / r81839;
        double r81841 = r81840 - r81829;
        double r81842 = r81827 * r81841;
        return r81842;
}
↓
double f(double x) {
        double r81843 = 0.70711;
        double r81844 = 2.30753;
        double r81845 = x;
        double r81846 = 0.27061;
        double r81847 = r81845 * r81846;
        double r81848 = r81844 + r81847;
        double r81849 = 1.0;
        double r81850 = 0.99229;
        double r81851 = 0.04481;
        double r81852 = r81845 * r81851;
        double r81853 = r81850 + r81852;
        double r81854 = r81845 * r81853;
        double r81855 = r81849 + r81854;
        double r81856 = r81848 / r81855;
        double r81857 = r81856 - r81845;
        double r81858 = r81843 * r81857;
        return r81858;
}

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 2020001 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x)))