Average Error: 4.4 → 0.0
Time: 23.6s
Precision: 64
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
↓
\[\sqrt{1 + e^{x}}\]
\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}
↓
\sqrt{1 + e^{x}}
double f(double x) {
        double r552544 = 2.0;
        double r552545 = x;
        double r552546 = r552544 * r552545;
        double r552547 = exp(r552546);
        double r552548 = 1.0;
        double r552549 = r552547 - r552548;
        double r552550 = exp(r552545);
        double r552551 = r552550 - r552548;
        double r552552 = r552549 / r552551;
        double r552553 = sqrt(r552552);
        return r552553;
}
↓
double f(double x) {
        double r552554 = 1.0;
        double r552555 = x;
        double r552556 = exp(r552555);
        double r552557 = r552554 + r552556;
        double r552558 = sqrt(r552557);
        return r552558;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019151 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))