Average Error: 4.4 → 0.1
Time: 26.6s
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 r943339 = 2.0;
        double r943340 = x;
        double r943341 = r943339 * r943340;
        double r943342 = exp(r943341);
        double r943343 = 1.0;
        double r943344 = r943342 - r943343;
        double r943345 = exp(r943340);
        double r943346 = r943345 - r943343;
        double r943347 = r943344 / r943346;
        double r943348 = sqrt(r943347);
        return r943348;
}
↓
double f(double x) {
        double r943349 = x;
        double r943350 = exp(r943349);
        double r943351 = 1.0;
        double r943352 = r943350 + r943351;
        double r943353 = sqrt(r943352);
        return r943353;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.4

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))