Average Error: 0.0 → 0.0
Time: 17.8s
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 r97751 = 0.70711;
        double r97752 = 2.30753;
        double r97753 = x;
        double r97754 = 0.27061;
        double r97755 = r97753 * r97754;
        double r97756 = r97752 + r97755;
        double r97757 = 1.0;
        double r97758 = 0.99229;
        double r97759 = 0.04481;
        double r97760 = r97753 * r97759;
        double r97761 = r97758 + r97760;
        double r97762 = r97753 * r97761;
        double r97763 = r97757 + r97762;
        double r97764 = r97756 / r97763;
        double r97765 = r97764 - r97753;
        double r97766 = r97751 * r97765;
        return r97766;
}
↓
double f(double x) {
        double r97767 = 0.70711;
        double r97768 = 2.30753;
        double r97769 = x;
        double r97770 = 0.27061;
        double r97771 = r97769 * r97770;
        double r97772 = r97768 + r97771;
        double r97773 = 1.0;
        double r97774 = 0.99229;
        double r97775 = 0.04481;
        double r97776 = r97769 * r97775;
        double r97777 = r97774 + r97776;
        double r97778 = r97769 * r97777;
        double r97779 = r97773 + r97778;
        double r97780 = r97772 / r97779;
        double r97781 = r97780 - r97769;
        double r97782 = r97767 * r97781;
        return r97782;
}

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 2020042 +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)))