Average Error: 4.2 → 0.1
Time: 30.7s
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 r803797 = 2.0;
        double r803798 = x;
        double r803799 = r803797 * r803798;
        double r803800 = exp(r803799);
        double r803801 = 1.0;
        double r803802 = r803800 - r803801;
        double r803803 = exp(r803798);
        double r803804 = r803803 - r803801;
        double r803805 = r803802 / r803804;
        double r803806 = sqrt(r803805);
        return r803806;
}
↓
double f(double x) {
        double r803807 = x;
        double r803808 = exp(r803807);
        double r803809 = 1.0;
        double r803810 = r803808 + r803809;
        double r803811 = sqrt(r803810);
        return r803811;
}

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 2019128 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))