Average Error: 0.0 → 0.0
Time: 2.9s
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 r91739 = 0.70711;
        double r91740 = 2.30753;
        double r91741 = x;
        double r91742 = 0.27061;
        double r91743 = r91741 * r91742;
        double r91744 = r91740 + r91743;
        double r91745 = 1.0;
        double r91746 = 0.99229;
        double r91747 = 0.04481;
        double r91748 = r91741 * r91747;
        double r91749 = r91746 + r91748;
        double r91750 = r91741 * r91749;
        double r91751 = r91745 + r91750;
        double r91752 = r91744 / r91751;
        double r91753 = r91752 - r91741;
        double r91754 = r91739 * r91753;
        return r91754;
}
↓
double f(double x) {
        double r91755 = 0.70711;
        double r91756 = 2.30753;
        double r91757 = x;
        double r91758 = 0.27061;
        double r91759 = r91757 * r91758;
        double r91760 = r91756 + r91759;
        double r91761 = 1.0;
        double r91762 = 0.99229;
        double r91763 = 0.04481;
        double r91764 = r91757 * r91763;
        double r91765 = r91762 + r91764;
        double r91766 = r91757 * r91765;
        double r91767 = r91761 + r91766;
        double r91768 = r91760 / r91767;
        double r91769 = r91768 - r91757;
        double r91770 = r91755 * r91769;
        return r91770;
}

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 2020036 
(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)))