Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} + 0.707110000000000016 \cdot \left(-x\right)\]
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 \frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} + 0.707110000000000016 \cdot \left(-x\right)
double f(double x) {
        double r122829 = 0.70711;
        double r122830 = 2.30753;
        double r122831 = x;
        double r122832 = 0.27061;
        double r122833 = r122831 * r122832;
        double r122834 = r122830 + r122833;
        double r122835 = 1.0;
        double r122836 = 0.99229;
        double r122837 = 0.04481;
        double r122838 = r122831 * r122837;
        double r122839 = r122836 + r122838;
        double r122840 = r122831 * r122839;
        double r122841 = r122835 + r122840;
        double r122842 = r122834 / r122841;
        double r122843 = r122842 - r122831;
        double r122844 = r122829 * r122843;
        return r122844;
}
↓
double f(double x) {
        double r122845 = 0.70711;
        double r122846 = 2.30753;
        double r122847 = x;
        double r122848 = 0.27061;
        double r122849 = r122847 * r122848;
        double r122850 = r122846 + r122849;
        double r122851 = 1.0;
        double r122852 = 0.99229;
        double r122853 = 0.04481;
        double r122854 = r122847 * r122853;
        double r122855 = r122852 + r122854;
        double r122856 = r122847 * r122855;
        double r122857 = r122851 + r122856;
        double r122858 = r122850 / r122857;
        double r122859 = r122845 * r122858;
        double r122860 = -r122847;
        double r122861 = r122845 * r122860;
        double r122862 = r122859 + r122861;
        return r122862;
}

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. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020025 
(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)))