Average Error: 0.0 → 0.0
Time: 9.9s
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 r92790 = 0.70711;
        double r92791 = 2.30753;
        double r92792 = x;
        double r92793 = 0.27061;
        double r92794 = r92792 * r92793;
        double r92795 = r92791 + r92794;
        double r92796 = 1.0;
        double r92797 = 0.99229;
        double r92798 = 0.04481;
        double r92799 = r92792 * r92798;
        double r92800 = r92797 + r92799;
        double r92801 = r92792 * r92800;
        double r92802 = r92796 + r92801;
        double r92803 = r92795 / r92802;
        double r92804 = r92803 - r92792;
        double r92805 = r92790 * r92804;
        return r92805;
}
↓
double f(double x) {
        double r92806 = 0.70711;
        double r92807 = 2.30753;
        double r92808 = x;
        double r92809 = 0.27061;
        double r92810 = r92808 * r92809;
        double r92811 = r92807 + r92810;
        double r92812 = 1.0;
        double r92813 = 0.99229;
        double r92814 = 0.04481;
        double r92815 = r92808 * r92814;
        double r92816 = r92813 + r92815;
        double r92817 = r92808 * r92816;
        double r92818 = r92812 + r92817;
        double r92819 = r92811 / r92818;
        double r92820 = r92819 - r92808;
        double r92821 = r92806 * r92820;
        return r92821;
}

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 2020046 +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)))