Average Error: 0.0 → 0.0
Time: 2.4s
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 r81808 = 0.70711;
        double r81809 = 2.30753;
        double r81810 = x;
        double r81811 = 0.27061;
        double r81812 = r81810 * r81811;
        double r81813 = r81809 + r81812;
        double r81814 = 1.0;
        double r81815 = 0.99229;
        double r81816 = 0.04481;
        double r81817 = r81810 * r81816;
        double r81818 = r81815 + r81817;
        double r81819 = r81810 * r81818;
        double r81820 = r81814 + r81819;
        double r81821 = r81813 / r81820;
        double r81822 = r81821 - r81810;
        double r81823 = r81808 * r81822;
        return r81823;
}
↓
double f(double x) {
        double r81824 = 0.70711;
        double r81825 = 2.30753;
        double r81826 = x;
        double r81827 = 0.27061;
        double r81828 = r81826 * r81827;
        double r81829 = r81825 + r81828;
        double r81830 = 1.0;
        double r81831 = 0.99229;
        double r81832 = 0.04481;
        double r81833 = r81826 * r81832;
        double r81834 = r81831 + r81833;
        double r81835 = r81826 * r81834;
        double r81836 = r81830 + r81835;
        double r81837 = r81829 / r81836;
        double r81838 = r81837 - r81826;
        double r81839 = r81824 * r81838;
        return r81839;
}

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)))