Average Error: 4.2 → 0.1
Time: 23.6s
Precision: 64
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
↓
\[\sqrt{e^{x} + 1}\]
\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}
↓
\sqrt{e^{x} + 1}
double f(double x) {
        double r845963 = 2.0;
        double r845964 = x;
        double r845965 = r845963 * r845964;
        double r845966 = exp(r845965);
        double r845967 = 1.0;
        double r845968 = r845966 - r845967;
        double r845969 = exp(r845964);
        double r845970 = r845969 - r845967;
        double r845971 = r845968 / r845970;
        double r845972 = sqrt(r845971);
        return r845972;
}
↓
double f(double x) {
        double r845973 = x;
        double r845974 = exp(r845973);
        double r845975 = 1.0;
        double r845976 = r845974 + r845975;
        double r845977 = sqrt(r845976);
        return r845977;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.2

    \[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\sqrt{e^{x} + 1}}\]

  3. Final simplification0.1

    \[\leadsto \sqrt{e^{x} + 1}\]

Reproduce

herbie shell --seed 2019135 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))