Average Error: 0.0 → 0.0
Time: 10.9s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)} - x\right)\]
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(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)} - x\right)
double f(double x) {
        double r5093749 = 0.70711;
        double r5093750 = 2.30753;
        double r5093751 = x;
        double r5093752 = 0.27061;
        double r5093753 = r5093751 * r5093752;
        double r5093754 = r5093750 + r5093753;
        double r5093755 = 1.0;
        double r5093756 = 0.99229;
        double r5093757 = 0.04481;
        double r5093758 = r5093751 * r5093757;
        double r5093759 = r5093756 + r5093758;
        double r5093760 = r5093751 * r5093759;
        double r5093761 = r5093755 + r5093760;
        double r5093762 = r5093754 / r5093761;
        double r5093763 = r5093762 - r5093751;
        double r5093764 = r5093749 * r5093763;
        return r5093764;
}
↓
double f(double x) {
        double r5093765 = 0.70711;
        double r5093766 = 2.30753;
        double r5093767 = x;
        double r5093768 = 0.27061;
        double r5093769 = r5093767 * r5093768;
        double r5093770 = r5093766 + r5093769;
        double r5093771 = 1.0;
        double r5093772 = 0.04481;
        double r5093773 = r5093767 * r5093772;
        double r5093774 = 0.99229;
        double r5093775 = r5093773 + r5093774;
        double r5093776 = r5093767 * r5093775;
        double r5093777 = r5093771 + r5093776;
        double r5093778 = r5093770 / r5093777;
        double r5093779 = r5093778 - r5093767;
        double r5093780 = r5093765 * r5093779;
        return r5093780;
}

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

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))