Average Error: 0.0 → 0.0
Time: 15.2s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[\left(-x\right) \cdot 0.7071100000000000163069557856942992657423 + \left(\sqrt{0.7071100000000000163069557856942992657423} \cdot \frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot x\right)}\right) \cdot \sqrt{0.7071100000000000163069557856942992657423}\]
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(-x\right) \cdot 0.7071100000000000163069557856942992657423 + \left(\sqrt{0.7071100000000000163069557856942992657423} \cdot \frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot x\right)}\right) \cdot \sqrt{0.7071100000000000163069557856942992657423}
double f(double x) {
        double r112809 = 0.70711;
        double r112810 = 2.30753;
        double r112811 = x;
        double r112812 = 0.27061;
        double r112813 = r112811 * r112812;
        double r112814 = r112810 + r112813;
        double r112815 = 1.0;
        double r112816 = 0.99229;
        double r112817 = 0.04481;
        double r112818 = r112811 * r112817;
        double r112819 = r112816 + r112818;
        double r112820 = r112811 * r112819;
        double r112821 = r112815 + r112820;
        double r112822 = r112814 / r112821;
        double r112823 = r112822 - r112811;
        double r112824 = r112809 * r112823;
        return r112824;
}
↓
double f(double x) {
        double r112825 = x;
        double r112826 = -r112825;
        double r112827 = 0.70711;
        double r112828 = r112826 * r112827;
        double r112829 = sqrt(r112827);
        double r112830 = 0.27061;
        double r112831 = r112825 * r112830;
        double r112832 = 2.30753;
        double r112833 = r112831 + r112832;
        double r112834 = 1.0;
        double r112835 = 0.99229;
        double r112836 = 0.04481;
        double r112837 = r112836 * r112825;
        double r112838 = r112835 + r112837;
        double r112839 = r112825 * r112838;
        double r112840 = r112834 + r112839;
        double r112841 = r112833 / r112840;
        double r112842 = r112829 * r112841;
        double r112843 = r112842 * r112829;
        double r112844 = r112828 + r112843;
        return r112844;
}

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

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

  6. Simplified0.0

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

  8. Applied add-sqr-sqrt0.0

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

  9. Applied *-un-lft-identity0.0

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

  10. Applied times-frac0.0

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

  11. Applied *-un-lft-identity0.0

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

  12. Applied times-frac0.5

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

  13. Simplified0.5

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

  14. Simplified0.0

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

  15. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(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)))