Average Error: 0.0 → 0.0
Time: 9.3s
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 r85773 = 0.70711;
        double r85774 = 2.30753;
        double r85775 = x;
        double r85776 = 0.27061;
        double r85777 = r85775 * r85776;
        double r85778 = r85774 + r85777;
        double r85779 = 1.0;
        double r85780 = 0.99229;
        double r85781 = 0.04481;
        double r85782 = r85775 * r85781;
        double r85783 = r85780 + r85782;
        double r85784 = r85775 * r85783;
        double r85785 = r85779 + r85784;
        double r85786 = r85778 / r85785;
        double r85787 = r85786 - r85775;
        double r85788 = r85773 * r85787;
        return r85788;
}
↓
double f(double x) {
        double r85789 = 0.70711;
        double r85790 = 2.30753;
        double r85791 = x;
        double r85792 = 0.27061;
        double r85793 = r85791 * r85792;
        double r85794 = r85790 + r85793;
        double r85795 = 1.0;
        double r85796 = 0.99229;
        double r85797 = 0.04481;
        double r85798 = r85791 * r85797;
        double r85799 = r85796 + r85798;
        double r85800 = r85791 * r85799;
        double r85801 = r85795 + r85800;
        double r85802 = r85794 / r85801;
        double r85803 = r85802 - r85791;
        double r85804 = r85789 * r85803;
        return r85804;
}

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 add-sqr-sqrt0.1

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

  4. Applied *-un-lft-identity0.1

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

  5. Applied times-frac0.1

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

  6. 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 2019291 
(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)))