Average Error: 0.0 → 0.0
Time: 4.0s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)
↓
0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)
double f(double x) {
        double r101865 = 0.70711;
        double r101866 = 2.30753;
        double r101867 = x;
        double r101868 = 0.27061;
        double r101869 = r101867 * r101868;
        double r101870 = r101866 + r101869;
        double r101871 = 1.0;
        double r101872 = 0.99229;
        double r101873 = 0.04481;
        double r101874 = r101867 * r101873;
        double r101875 = r101872 + r101874;
        double r101876 = r101867 * r101875;
        double r101877 = r101871 + r101876;
        double r101878 = r101870 / r101877;
        double r101879 = r101878 - r101867;
        double r101880 = r101865 * r101879;
        return r101880;
}
↓
double f(double x) {
        double r101881 = 0.70711;
        double r101882 = 2.30753;
        double r101883 = x;
        double r101884 = 0.27061;
        double r101885 = r101883 * r101884;
        double r101886 = r101882 + r101885;
        double r101887 = 1.0;
        double r101888 = 0.99229;
        double r101889 = 0.04481;
        double r101890 = r101883 * r101889;
        double r101891 = r101888 + r101890;
        double r101892 = r101883 * r101891;
        double r101893 = r101887 + r101892;
        double r101894 = r101886 / r101893;
        double r101895 = r101894 - r101883;
        double r101896 = r101881 * r101895;
        return r101896;
}

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

    \[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]

  2. Final simplification0.0

    \[\leadsto 0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x)))