Average Error: 4.5 → 0.1
Time: 19.4s
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 r543053 = 2.0;
        double r543054 = x;
        double r543055 = r543053 * r543054;
        double r543056 = exp(r543055);
        double r543057 = 1.0;
        double r543058 = r543056 - r543057;
        double r543059 = exp(r543054);
        double r543060 = r543059 - r543057;
        double r543061 = r543058 / r543060;
        double r543062 = sqrt(r543061);
        return r543062;
}
↓
double f(double x) {
        double r543063 = x;
        double r543064 = exp(r543063);
        double r543065 = 1.0;
        double r543066 = r543064 + r543065;
        double r543067 = sqrt(r543066);
        return r543067;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.5

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019137 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))