Average Error: 0.0 → 0.0
Time: 18.1s
Precision: 64
\[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
↓
\[\left(-x\right) \cdot 0.70711 + \frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} \cdot 0.70711\]
0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)
↓
\left(-x\right) \cdot 0.70711 + \frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} \cdot 0.70711
double f(double x) {
        double r5402688 = 0.70711;
        double r5402689 = 2.30753;
        double r5402690 = x;
        double r5402691 = 0.27061;
        double r5402692 = r5402690 * r5402691;
        double r5402693 = r5402689 + r5402692;
        double r5402694 = 1.0;
        double r5402695 = 0.99229;
        double r5402696 = 0.04481;
        double r5402697 = r5402690 * r5402696;
        double r5402698 = r5402695 + r5402697;
        double r5402699 = r5402690 * r5402698;
        double r5402700 = r5402694 + r5402699;
        double r5402701 = r5402693 / r5402700;
        double r5402702 = r5402701 - r5402690;
        double r5402703 = r5402688 * r5402702;
        return r5402703;
}
↓
double f(double x) {
        double r5402704 = x;
        double r5402705 = -r5402704;
        double r5402706 = 0.70711;
        double r5402707 = r5402705 * r5402706;
        double r5402708 = 2.30753;
        double r5402709 = 0.27061;
        double r5402710 = r5402704 * r5402709;
        double r5402711 = r5402708 + r5402710;
        double r5402712 = 1.0;
        double r5402713 = 0.04481;
        double r5402714 = r5402704 * r5402713;
        double r5402715 = 0.99229;
        double r5402716 = r5402714 + r5402715;
        double r5402717 = r5402704 * r5402716;
        double r5402718 = r5402712 + r5402717;
        double r5402719 = r5402711 / r5402718;
        double r5402720 = r5402719 * r5402706;
        double r5402721 = r5402707 + r5402720;
        return r5402721;
}

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

    \[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto 0.70711 \cdot \color{blue}{\left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} + \left(-x\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{0.70711 \cdot \frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} + 0.70711 \cdot \left(-x\right)}\]

  5. Final simplification0.0

    \[\leadsto \left(-x\right) \cdot 0.70711 + \frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(x \cdot 0.04481 + 0.99229\right)} \cdot 0.70711\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))