Average Error: 0.0 → 0.0
Time: 17.7s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} \cdot 0.7071100000000000163069557856942992657423 + 0.7071100000000000163069557856942992657423 \cdot \left(-x\right)\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} \cdot 0.7071100000000000163069557856942992657423 + 0.7071100000000000163069557856942992657423 \cdot \left(-x\right)
double f(double x) {
        double r98844 = 0.70711;
        double r98845 = 2.30753;
        double r98846 = x;
        double r98847 = 0.27061;
        double r98848 = r98846 * r98847;
        double r98849 = r98845 + r98848;
        double r98850 = 1.0;
        double r98851 = 0.99229;
        double r98852 = 0.04481;
        double r98853 = r98846 * r98852;
        double r98854 = r98851 + r98853;
        double r98855 = r98846 * r98854;
        double r98856 = r98850 + r98855;
        double r98857 = r98849 / r98856;
        double r98858 = r98857 - r98846;
        double r98859 = r98844 * r98858;
        return r98859;
}
↓
double f(double x) {
        double r98860 = 2.30753;
        double r98861 = x;
        double r98862 = 0.27061;
        double r98863 = r98861 * r98862;
        double r98864 = r98860 + r98863;
        double r98865 = 1.0;
        double r98866 = 0.99229;
        double r98867 = 0.04481;
        double r98868 = r98861 * r98867;
        double r98869 = r98866 + r98868;
        double r98870 = r98861 * r98869;
        double r98871 = r98865 + r98870;
        double r98872 = r98864 / r98871;
        double r98873 = 0.70711;
        double r98874 = r98872 * r98873;
        double r98875 = -r98861;
        double r98876 = r98873 * r98875;
        double r98877 = r98874 + r98876;
        return r98877;
}

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. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019235 
(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)))