Average Error: 0.0 → 0.0
Time: 5.1s
Precision: 64
\[e^{x + 1} + 1\]
\[1 + \sqrt[3]{e^{\left(x + 1\right) \cdot 3}}\]
e^{x + 1} + 1
1 + \sqrt[3]{e^{\left(x + 1\right) \cdot 3}}
double f(double x) {
        double r45589867 = x;
        double r45589868 = 1.0;
        double r45589869 = r45589867 + r45589868;
        double r45589870 = exp(r45589869);
        double r45589871 = r45589870 + r45589868;
        return r45589871;
}

double f(double x) {
        double r45589872 = 1.0;
        double r45589873 = x;
        double r45589874 = r45589873 + r45589872;
        double r45589875 = 3.0;
        double r45589876 = r45589874 * r45589875;
        double r45589877 = exp(r45589876);
        double r45589878 = cbrt(r45589877);
        double r45589879 = r45589872 + r45589878;
        return r45589879;
}

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

    \[e^{x + 1} + 1\]
  2. Using strategy rm
  3. Applied add-cbrt-cube0.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(e^{x + 1} \cdot e^{x + 1}\right) \cdot e^{x + 1}}} + 1\]
  4. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{e^{3 \cdot \left(x + 1\right)}}} + 1\]
  5. Final simplification0.0

    \[\leadsto 1 + \sqrt[3]{e^{\left(x + 1\right) \cdot 3}}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "exp(x+1)+1"
  (+ (exp (+ x 1.0)) 1.0))