Average Error: 4.2 → 0.1
Time: 17.8s
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 r373840 = 2.0;
        double r373841 = x;
        double r373842 = r373840 * r373841;
        double r373843 = exp(r373842);
        double r373844 = 1.0;
        double r373845 = r373843 - r373844;
        double r373846 = exp(r373841);
        double r373847 = r373846 - r373844;
        double r373848 = r373845 / r373847;
        double r373849 = sqrt(r373848);
        return r373849;
}
↓
double f(double x) {
        double r373850 = x;
        double r373851 = exp(r373850);
        double r373852 = 1.0;
        double r373853 = r373851 + r373852;
        double r373854 = sqrt(r373853);
        return r373854;
}

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))))