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;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.0

$e^{x + 1} + 1$
2. Using strategy rm

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