Average Error: 0.0 → 0.0
Time: 14.0s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[\left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right) \cdot 0.7071100000000000163069557856942992657423\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
\left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right) \cdot 0.7071100000000000163069557856942992657423
double f(double x) {
        double r67783 = 0.70711;
        double r67784 = 2.30753;
        double r67785 = x;
        double r67786 = 0.27061;
        double r67787 = r67785 * r67786;
        double r67788 = r67784 + r67787;
        double r67789 = 1.0;
        double r67790 = 0.99229;
        double r67791 = 0.04481;
        double r67792 = r67785 * r67791;
        double r67793 = r67790 + r67792;
        double r67794 = r67785 * r67793;
        double r67795 = r67789 + r67794;
        double r67796 = r67788 / r67795;
        double r67797 = r67796 - r67785;
        double r67798 = r67783 * r67797;
        return r67798;
}
↓
double f(double x) {
        double r67799 = 2.30753;
        double r67800 = x;
        double r67801 = 0.27061;
        double r67802 = r67800 * r67801;
        double r67803 = r67799 + r67802;
        double r67804 = 1.0;
        double r67805 = 0.99229;
        double r67806 = 0.04481;
        double r67807 = r67800 * r67806;
        double r67808 = r67805 + r67807;
        double r67809 = r67800 * r67808;
        double r67810 = r67804 + r67809;
        double r67811 = r67803 / r67810;
        double r67812 = r67811 - r67800;
        double r67813 = 0.70711;
        double r67814 = r67812 * r67813;
        return r67814;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019294 
(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)))