Average Error: 4.2 → 0.1
Time: 23.1s
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 r952330 = 2.0;
        double r952331 = x;
        double r952332 = r952330 * r952331;
        double r952333 = exp(r952332);
        double r952334 = 1.0;
        double r952335 = r952333 - r952334;
        double r952336 = exp(r952331);
        double r952337 = r952336 - r952334;
        double r952338 = r952335 / r952337;
        double r952339 = sqrt(r952338);
        return r952339;
}
↓
double f(double x) {
        double r952340 = x;
        double r952341 = exp(r952340);
        double r952342 = 1.0;
        double r952343 = r952341 + r952342;
        double r952344 = sqrt(r952343);
        return r952344;
}

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 2019168 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))