Average Error: 0.0 → 0.0
Time: 4.0s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[\left(0.7071100000000000163069557856942992657423 \cdot \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right)\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} + 0.7071100000000000163069557856942992657423 \cdot \left(-x\right)\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
\left(0.7071100000000000163069557856942992657423 \cdot \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right)\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} + 0.7071100000000000163069557856942992657423 \cdot \left(-x\right)
double f(double x) {
        double r125724 = 0.70711;
        double r125725 = 2.30753;
        double r125726 = x;
        double r125727 = 0.27061;
        double r125728 = r125726 * r125727;
        double r125729 = r125725 + r125728;
        double r125730 = 1.0;
        double r125731 = 0.99229;
        double r125732 = 0.04481;
        double r125733 = r125726 * r125732;
        double r125734 = r125731 + r125733;
        double r125735 = r125726 * r125734;
        double r125736 = r125730 + r125735;
        double r125737 = r125729 / r125736;
        double r125738 = r125737 - r125726;
        double r125739 = r125724 * r125738;
        return r125739;
}
↓
double f(double x) {
        double r125740 = 0.70711;
        double r125741 = 2.30753;
        double r125742 = x;
        double r125743 = 0.27061;
        double r125744 = r125742 * r125743;
        double r125745 = r125741 + r125744;
        double r125746 = r125740 * r125745;
        double r125747 = 1.0;
        double r125748 = 1.0;
        double r125749 = 0.99229;
        double r125750 = 0.04481;
        double r125751 = r125742 * r125750;
        double r125752 = r125749 + r125751;
        double r125753 = r125742 * r125752;
        double r125754 = r125748 + r125753;
        double r125755 = r125747 / r125754;
        double r125756 = r125746 * r125755;
        double r125757 = -r125742;
        double r125758 = r125740 * r125757;
        double r125759 = r125756 + r125758;
        return r125759;
}

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

    \[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \color{blue}{\left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} + \left(-x\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{0.7071100000000000163069557856942992657423 \cdot \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} + 0.7071100000000000163069557856942992657423 \cdot \left(-x\right)}\]
  5. Using strategy rm

  6. Applied div-inv0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \color{blue}{\left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}\right)} + 0.7071100000000000163069557856942992657423 \cdot \left(-x\right)\]

  7. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(0.7071100000000000163069557856942992657423 \cdot \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right)\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}} + 0.7071100000000000163069557856942992657423 \cdot \left(-x\right)\]

  8. Final simplification0.0

    \[\leadsto \left(0.7071100000000000163069557856942992657423 \cdot \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right)\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} + 0.7071100000000000163069557856942992657423 \cdot \left(-x\right)\]

Reproduce

herbie shell --seed 2019347 
(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)))