Average Error: 0.0 → 0.1
Time: 8.5s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\frac{\frac{1}{\frac{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}{2.30753 + x \cdot 0.27061000000000002}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\frac{\frac{1}{\frac{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}{2.30753 + x \cdot 0.27061000000000002}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x
double f(double x) {
        double r69770 = 2.30753;
        double r69771 = x;
        double r69772 = 0.27061;
        double r69773 = r69771 * r69772;
        double r69774 = r69770 + r69773;
        double r69775 = 1.0;
        double r69776 = 0.99229;
        double r69777 = 0.04481;
        double r69778 = r69771 * r69777;
        double r69779 = r69776 + r69778;
        double r69780 = r69771 * r69779;
        double r69781 = r69775 + r69780;
        double r69782 = r69774 / r69781;
        double r69783 = r69782 - r69771;
        return r69783;
}
↓
double f(double x) {
        double r69784 = 1.0;
        double r69785 = 1.0;
        double r69786 = x;
        double r69787 = 0.99229;
        double r69788 = 0.04481;
        double r69789 = r69786 * r69788;
        double r69790 = r69787 + r69789;
        double r69791 = r69786 * r69790;
        double r69792 = r69785 + r69791;
        double r69793 = sqrt(r69792);
        double r69794 = 2.30753;
        double r69795 = 0.27061;
        double r69796 = r69786 * r69795;
        double r69797 = r69794 + r69796;
        double r69798 = r69793 / r69797;
        double r69799 = r69784 / r69798;
        double r69800 = r69799 / r69793;
        double r69801 = r69800 - r69786;
        return r69801;
}

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

    \[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.1

    \[\leadsto \frac{2.30753 + x \cdot 0.27061000000000002}{\color{blue}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} \cdot \sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}} - x\]

  4. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}} - x\]
  5. Using strategy rm

  6. Applied clear-num0.1

    \[\leadsto \frac{\color{blue}{\frac{1}{\frac{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}{2.30753 + x \cdot 0.27061000000000002}}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\]

  7. Final simplification0.1

    \[\leadsto \frac{\frac{1}{\frac{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}{2.30753 + x \cdot 0.27061000000000002}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x))