Average Error: 0.0 → 0.0
Time: 13.4s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.04481000000000000260680366181986755691469 \cdot {x}^{2} + 0.992290000000000005364597654988756403327 \cdot x\right)} - x\right)\]
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 + \left(0.04481000000000000260680366181986755691469 \cdot {x}^{2} + 0.992290000000000005364597654988756403327 \cdot x\right)} - x\right)
double f(double x) {
        double r81146 = 0.70711;
        double r81147 = 2.30753;
        double r81148 = x;
        double r81149 = 0.27061;
        double r81150 = r81148 * r81149;
        double r81151 = r81147 + r81150;
        double r81152 = 1.0;
        double r81153 = 0.99229;
        double r81154 = 0.04481;
        double r81155 = r81148 * r81154;
        double r81156 = r81153 + r81155;
        double r81157 = r81148 * r81156;
        double r81158 = r81152 + r81157;
        double r81159 = r81151 / r81158;
        double r81160 = r81159 - r81148;
        double r81161 = r81146 * r81160;
        return r81161;
}
↓
double f(double x) {
        double r81162 = 0.70711;
        double r81163 = 2.30753;
        double r81164 = x;
        double r81165 = 0.27061;
        double r81166 = r81164 * r81165;
        double r81167 = r81163 + r81166;
        double r81168 = 1.0;
        double r81169 = 0.04481;
        double r81170 = 2.0;
        double r81171 = pow(r81164, r81170);
        double r81172 = r81169 * r81171;
        double r81173 = 0.99229;
        double r81174 = r81173 * r81164;
        double r81175 = r81172 + r81174;
        double r81176 = r81168 + r81175;
        double r81177 = r81167 / r81176;
        double r81178 = r81177 - r81164;
        double r81179 = r81162 * r81178;
        return r81179;
}

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. Taylor expanded around 0 0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \color{blue}{\left(0.04481000000000000260680366181986755691469 \cdot {x}^{2} + 0.992290000000000005364597654988756403327 \cdot x\right)}} - x\right)\]

  3. Final simplification0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.04481000000000000260680366181986755691469 \cdot {x}^{2} + 0.992290000000000005364597654988756403327 \cdot x\right)} - x\right)\]

Reproduce

herbie shell --seed 2019212 
(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)))