Average Error: 0.0 → 0.1
Time: 8.2s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\frac{1}{\sqrt{\left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x + 1}} \cdot \frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{\sqrt{\left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x + 1}} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\frac{1}{\sqrt{\left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x + 1}} \cdot \frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{\sqrt{\left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x + 1}} - x
double f(double x) {
        double r63724 = 2.30753;
        double r63725 = x;
        double r63726 = 0.27061;
        double r63727 = r63725 * r63726;
        double r63728 = r63724 + r63727;
        double r63729 = 1.0;
        double r63730 = 0.99229;
        double r63731 = 0.04481;
        double r63732 = r63725 * r63731;
        double r63733 = r63730 + r63732;
        double r63734 = r63725 * r63733;
        double r63735 = r63729 + r63734;
        double r63736 = r63728 / r63735;
        double r63737 = r63736 - r63725;
        return r63737;
}
↓
double f(double x) {
        double r63738 = 1.0;
        double r63739 = 0.99229;
        double r63740 = x;
        double r63741 = 0.04481;
        double r63742 = r63740 * r63741;
        double r63743 = r63739 + r63742;
        double r63744 = r63743 * r63740;
        double r63745 = 1.0;
        double r63746 = r63744 + r63745;
        double r63747 = sqrt(r63746);
        double r63748 = r63738 / r63747;
        double r63749 = 0.27061;
        double r63750 = r63740 * r63749;
        double r63751 = 2.30753;
        double r63752 = r63750 + r63751;
        double r63753 = r63752 / r63747;
        double r63754 = r63748 * r63753;
        double r63755 = r63754 - r63740;
        return r63755;
}

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

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

  2. Simplified0.0

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

  4. Applied add-sqr-sqrt0.1

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

  5. Applied *-un-lft-identity0.1

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

  6. Applied times-frac0.1

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

  7. Simplified0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))