Average Error: 0.0 → 0.0
Time: 20.4s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} \cdot 0.7071100000000000163069557856942992657423 + 0.7071100000000000163069557856942992657423 \cdot \left(-x\right)\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} \cdot 0.7071100000000000163069557856942992657423 + 0.7071100000000000163069557856942992657423 \cdot \left(-x\right)
double f(double x) {
        double r85694 = 0.70711;
        double r85695 = 2.30753;
        double r85696 = x;
        double r85697 = 0.27061;
        double r85698 = r85696 * r85697;
        double r85699 = r85695 + r85698;
        double r85700 = 1.0;
        double r85701 = 0.99229;
        double r85702 = 0.04481;
        double r85703 = r85696 * r85702;
        double r85704 = r85701 + r85703;
        double r85705 = r85696 * r85704;
        double r85706 = r85700 + r85705;
        double r85707 = r85699 / r85706;
        double r85708 = r85707 - r85696;
        double r85709 = r85694 * r85708;
        return r85709;
}
↓
double f(double x) {
        double r85710 = 2.30753;
        double r85711 = x;
        double r85712 = 0.27061;
        double r85713 = r85711 * r85712;
        double r85714 = r85710 + r85713;
        double r85715 = 1.0;
        double r85716 = 0.99229;
        double r85717 = 0.04481;
        double r85718 = r85711 * r85717;
        double r85719 = r85716 + r85718;
        double r85720 = r85711 * r85719;
        double r85721 = r85715 + r85720;
        double r85722 = r85714 / r85721;
        double r85723 = 0.70711;
        double r85724 = r85722 * r85723;
        double r85725 = -r85711;
        double r85726 = r85723 * r85725;
        double r85727 = r85724 + r85726;
        return r85727;
}

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. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(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)))