Average Error: 0.0 → 0.0
Time: 16.0s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{0.7071100000000000163069557856942992657423}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} + 0.7071100000000000163069557856942992657423 \cdot \left(-x\right)\]
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(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{0.7071100000000000163069557856942992657423}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} + 0.7071100000000000163069557856942992657423 \cdot \left(-x\right)
double f(double x) {
        double r91680 = 0.70711;
        double r91681 = 2.30753;
        double r91682 = x;
        double r91683 = 0.27061;
        double r91684 = r91682 * r91683;
        double r91685 = r91681 + r91684;
        double r91686 = 1.0;
        double r91687 = 0.99229;
        double r91688 = 0.04481;
        double r91689 = r91682 * r91688;
        double r91690 = r91687 + r91689;
        double r91691 = r91682 * r91690;
        double r91692 = r91686 + r91691;
        double r91693 = r91685 / r91692;
        double r91694 = r91693 - r91682;
        double r91695 = r91680 * r91694;
        return r91695;
}
↓
double f(double x) {
        double r91696 = 2.30753;
        double r91697 = x;
        double r91698 = 0.27061;
        double r91699 = r91697 * r91698;
        double r91700 = r91696 + r91699;
        double r91701 = 0.70711;
        double r91702 = 1.0;
        double r91703 = 0.99229;
        double r91704 = 0.04481;
        double r91705 = r91697 * r91704;
        double r91706 = r91703 + r91705;
        double r91707 = r91697 * r91706;
        double r91708 = r91702 + r91707;
        double r91709 = r91701 / r91708;
        double r91710 = r91700 * r91709;
        double r91711 = -r91697;
        double r91712 = r91701 * r91711;
        double r91713 = r91710 + r91712;
        return r91713;
}

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. Using strategy rm

  7. Applied div-inv0.0

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

  8. Applied associate-*l*0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.707110000000000016 (- (/ (+ 2.30753 (* x 0.27061000000000002)) (+ 1 (* x (+ 0.992290000000000005 (* x 0.044810000000000003))))) x)))