Average Error: 0.0 → 0.1
Time: 3.2s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\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
double f(double x) {
        double r50849 = 2.30753;
        double r50850 = x;
        double r50851 = 0.27061;
        double r50852 = r50850 * r50851;
        double r50853 = r50849 + r50852;
        double r50854 = 1.0;
        double r50855 = 0.99229;
        double r50856 = 0.04481;
        double r50857 = r50850 * r50856;
        double r50858 = r50855 + r50857;
        double r50859 = r50850 * r50858;
        double r50860 = r50854 + r50859;
        double r50861 = r50853 / r50860;
        double r50862 = r50861 - r50850;
        return r50862;
}
↓
double f(double x) {
        double r50863 = 2.30753;
        double r50864 = x;
        double r50865 = 0.27061;
        double r50866 = r50864 * r50865;
        double r50867 = r50863 + r50866;
        double r50868 = 1.0;
        double r50869 = 0.99229;
        double r50870 = 0.04481;
        double r50871 = r50864 * r50870;
        double r50872 = r50869 + r50871;
        double r50873 = r50864 * r50872;
        double r50874 = r50868 + r50873;
        double r50875 = sqrt(r50874);
        double r50876 = r50867 / r50875;
        double r50877 = r50876 / r50875;
        double r50878 = r50877 - r50864;
        return r50878;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 
(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))