Average Error: 4.3 → 0.1
Time: 14.0s
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 r284737 = 2.0;
        double r284738 = x;
        double r284739 = r284737 * r284738;
        double r284740 = exp(r284739);
        double r284741 = 1.0;
        double r284742 = r284740 - r284741;
        double r284743 = exp(r284738);
        double r284744 = r284743 - r284741;
        double r284745 = r284742 / r284744;
        double r284746 = sqrt(r284745);
        return r284746;
}
↓
double f(double x) {
        double r284747 = 1.0;
        double r284748 = x;
        double r284749 = exp(r284748);
        double r284750 = r284747 + r284749;
        double r284751 = sqrt(r284750);
        return r284751;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.3

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019146 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))