Average Error: 0.0 → 0.1
Time: 2.7s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\frac{\frac{1}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\frac{\frac{1}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}} - x
double f(double x) {
        double r64730 = 2.30753;
        double r64731 = x;
        double r64732 = 0.27061;
        double r64733 = r64731 * r64732;
        double r64734 = r64730 + r64733;
        double r64735 = 1.0;
        double r64736 = 0.99229;
        double r64737 = 0.04481;
        double r64738 = r64731 * r64737;
        double r64739 = r64736 + r64738;
        double r64740 = r64731 * r64739;
        double r64741 = r64735 + r64740;
        double r64742 = r64734 / r64741;
        double r64743 = r64742 - r64731;
        return r64743;
}
↓
double f(double x) {
        double r64744 = 1.0;
        double r64745 = 1.0;
        double r64746 = x;
        double r64747 = 0.99229;
        double r64748 = 0.04481;
        double r64749 = r64746 * r64748;
        double r64750 = r64747 + r64749;
        double r64751 = r64746 * r64750;
        double r64752 = r64745 + r64751;
        double r64753 = sqrt(r64752);
        double r64754 = r64744 / r64753;
        double r64755 = cbrt(r64753);
        double r64756 = r64755 * r64755;
        double r64757 = r64754 / r64756;
        double r64758 = 2.30753;
        double r64759 = 0.27061;
        double r64760 = r64746 * r64759;
        double r64761 = r64758 + r64760;
        double r64762 = r64761 / r64755;
        double r64763 = r64757 * r64762;
        double r64764 = r64763 - r64746;
        return r64764;
}

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-sqrt0.0

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

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

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

  5. Applied times-frac0.1

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

  7. Applied add-cube-cbrt0.1

    \[\leadsto \frac{1}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\color{blue}{\left(\sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}\right) \cdot \sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}} - x\]

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

    \[\leadsto \frac{1}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \frac{\color{blue}{1 \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}{\left(\sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}\right) \cdot \sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}} - x\]

  9. Applied times-frac0.1

    \[\leadsto \frac{1}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}\right)} - x\]

  10. Applied associate-*r*0.1

    \[\leadsto \color{blue}{\left(\frac{1}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \frac{1}{\sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}\right) \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}} - x\]

  11. Simplified0.1

    \[\leadsto \color{blue}{\frac{\frac{1}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}} - x\]

  12. Final simplification0.1

    \[\leadsto \frac{\frac{1}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}} - x\]

Reproduce

herbie shell --seed 2020056 
(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))