Average Error: 0.0 → 0.0
Time: 1.7s
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 r104745 = 0.70711;
        double r104746 = 2.30753;
        double r104747 = x;
        double r104748 = 0.27061;
        double r104749 = r104747 * r104748;
        double r104750 = r104746 + r104749;
        double r104751 = 1.0;
        double r104752 = 0.99229;
        double r104753 = 0.04481;
        double r104754 = r104747 * r104753;
        double r104755 = r104752 + r104754;
        double r104756 = r104747 * r104755;
        double r104757 = r104751 + r104756;
        double r104758 = r104750 / r104757;
        double r104759 = r104758 - r104747;
        double r104760 = r104745 * r104759;
        return r104760;
}
↓
double f(double x) {
        double r104761 = 0.70711;
        double r104762 = 2.30753;
        double r104763 = x;
        double r104764 = 0.27061;
        double r104765 = r104763 * r104764;
        double r104766 = r104762 + r104765;
        double r104767 = 1.0;
        double r104768 = 0.99229;
        double r104769 = 0.04481;
        double r104770 = r104763 * r104769;
        double r104771 = r104768 + r104770;
        double r104772 = r104763 * r104771;
        double r104773 = r104767 + r104772;
        double r104774 = r104766 / r104773;
        double r104775 = r104774 - r104763;
        double r104776 = r104761 * r104775;
        return r104776;
}

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 2019322 
(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)))