Average Error: 2.0 → 1.7
Time: 15.3s
Precision: 64
\[\frac{\sinh \left(x + 1\right) - 1}{\frac{1}{2}}\]
\[\frac{\frac{\left(\left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right) \cdot \left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right)\right) \cdot \left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right) - \left(1 \cdot 1\right) \cdot 1}{1 \cdot 1 + \left(\left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right) \cdot 1 + \left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right) \cdot \left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right)\right)}}{\frac{1}{2}}\]
\frac{\sinh \left(x + 1\right) - 1}{\frac{1}{2}}
\frac{\frac{\left(\left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right) \cdot \left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right)\right) \cdot \left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right) - \left(1 \cdot 1\right) \cdot 1}{1 \cdot 1 + \left(\left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right) \cdot 1 + \left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right) \cdot \left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right)\right)}}{\frac{1}{2}}
double f(double x) {
        double r35358855 = x;
        double r35358856 = 1.0;
        double r35358857 = r35358855 + r35358856;
        double r35358858 = sinh(r35358857);
        double r35358859 = r35358858 - r35358856;
        double r35358860 = 2.0;
        double r35358861 = r35358856 / r35358860;
        double r35358862 = r35358859 / r35358861;
        return r35358862;
}

double f(double x) {
        double r35358863 = 1.0;
        double r35358864 = cosh(r35358863);
        double r35358865 = x;
        double r35358866 = sinh(r35358865);
        double r35358867 = r35358864 * r35358866;
        double r35358868 = sinh(r35358863);
        double r35358869 = cosh(r35358865);
        double r35358870 = r35358868 * r35358869;
        double r35358871 = r35358867 + r35358870;
        double r35358872 = r35358871 * r35358871;
        double r35358873 = r35358872 * r35358871;
        double r35358874 = r35358863 * r35358863;
        double r35358875 = r35358874 * r35358863;
        double r35358876 = r35358873 - r35358875;
        double r35358877 = r35358871 * r35358863;
        double r35358878 = r35358877 + r35358872;
        double r35358879 = r35358874 + r35358878;
        double r35358880 = r35358876 / r35358879;
        double r35358881 = 2.0;
        double r35358882 = r35358863 / r35358881;
        double r35358883 = r35358880 / r35358882;
        return r35358883;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.0

    \[\frac{\sinh \left(x + 1\right) - 1}{\frac{1}{2}}\]
  2. Using strategy rm
  3. Applied sinh-sum2.0

    \[\leadsto \frac{\color{blue}{\left(\sinh x \cdot \cosh 1 + \cosh x \cdot \sinh 1\right)} - 1}{\frac{1}{2}}\]
  4. Using strategy rm
  5. Applied flip3--1.7

    \[\leadsto \frac{\color{blue}{\frac{{\left(\sinh x \cdot \cosh 1 + \cosh x \cdot \sinh 1\right)}^{3} - {1}^{3}}{\left(\sinh x \cdot \cosh 1 + \cosh x \cdot \sinh 1\right) \cdot \left(\sinh x \cdot \cosh 1 + \cosh x \cdot \sinh 1\right) + \left(1 \cdot 1 + \left(\sinh x \cdot \cosh 1 + \cosh x \cdot \sinh 1\right) \cdot 1\right)}}}{\frac{1}{2}}\]
  6. Simplified1.7

    \[\leadsto \frac{\frac{\color{blue}{\left(\left(\cosh x \cdot \sinh 1 + \cosh 1 \cdot \sinh x\right) \cdot \left(\cosh x \cdot \sinh 1 + \cosh 1 \cdot \sinh x\right)\right) \cdot \left(\cosh x \cdot \sinh 1 + \cosh 1 \cdot \sinh x\right) - 1 \cdot \left(1 \cdot 1\right)}}{\left(\sinh x \cdot \cosh 1 + \cosh x \cdot \sinh 1\right) \cdot \left(\sinh x \cdot \cosh 1 + \cosh x \cdot \sinh 1\right) + \left(1 \cdot 1 + \left(\sinh x \cdot \cosh 1 + \cosh x \cdot \sinh 1\right) \cdot 1\right)}}{\frac{1}{2}}\]
  7. Simplified1.7

    \[\leadsto \frac{\frac{\left(\left(\cosh x \cdot \sinh 1 + \cosh 1 \cdot \sinh x\right) \cdot \left(\cosh x \cdot \sinh 1 + \cosh 1 \cdot \sinh x\right)\right) \cdot \left(\cosh x \cdot \sinh 1 + \cosh 1 \cdot \sinh x\right) - 1 \cdot \left(1 \cdot 1\right)}{\color{blue}{\left(\left(\cosh x \cdot \sinh 1 + \cosh 1 \cdot \sinh x\right) \cdot \left(\cosh x \cdot \sinh 1 + \cosh 1 \cdot \sinh x\right) + 1 \cdot \left(\cosh x \cdot \sinh 1 + \cosh 1 \cdot \sinh x\right)\right) + 1 \cdot 1}}}{\frac{1}{2}}\]
  8. Final simplification1.7

    \[\leadsto \frac{\frac{\left(\left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right) \cdot \left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right)\right) \cdot \left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right) - \left(1 \cdot 1\right) \cdot 1}{1 \cdot 1 + \left(\left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right) \cdot 1 + \left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right) \cdot \left(\cosh 1 \cdot \sinh x + \sinh 1 \cdot \cosh x\right)\right)}}{\frac{1}{2}}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "(sinh(x+1)-1)/(1/2)"
  (/ (- (sinh (+ x 1.0)) 1.0) (/ 1.0 2.0)))