Average Error: 0.0 → 0.0
Time: 4.3s
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 r149838 = 0.70711;
        double r149839 = 2.30753;
        double r149840 = x;
        double r149841 = 0.27061;
        double r149842 = r149840 * r149841;
        double r149843 = r149839 + r149842;
        double r149844 = 1.0;
        double r149845 = 0.99229;
        double r149846 = 0.04481;
        double r149847 = r149840 * r149846;
        double r149848 = r149845 + r149847;
        double r149849 = r149840 * r149848;
        double r149850 = r149844 + r149849;
        double r149851 = r149843 / r149850;
        double r149852 = r149851 - r149840;
        double r149853 = r149838 * r149852;
        return r149853;
}
↓
double f(double x) {
        double r149854 = 0.70711;
        double r149855 = 2.30753;
        double r149856 = x;
        double r149857 = 0.27061;
        double r149858 = r149856 * r149857;
        double r149859 = r149855 + r149858;
        double r149860 = 1.0;
        double r149861 = 0.99229;
        double r149862 = 0.04481;
        double r149863 = r149856 * r149862;
        double r149864 = r149861 + r149863;
        double r149865 = r149856 * r149864;
        double r149866 = r149860 + r149865;
        double r149867 = r149859 / r149866;
        double r149868 = r149867 - r149856;
        double r149869 = r149854 * r149868;
        return r149869;
}

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 2019356 
(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)))