Average Error: 4.7 → 0.1
Time: 15.9s
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 r272727 = 2.0;
        double r272728 = x;
        double r272729 = r272727 * r272728;
        double r272730 = exp(r272729);
        double r272731 = 1.0;
        double r272732 = r272730 - r272731;
        double r272733 = exp(r272728);
        double r272734 = r272733 - r272731;
        double r272735 = r272732 / r272734;
        double r272736 = sqrt(r272735);
        return r272736;
}
↓
double f(double x) {
        double r272737 = x;
        double r272738 = exp(r272737);
        double r272739 = 1.0;
        double r272740 = r272738 + r272739;
        double r272741 = sqrt(r272740);
        return r272741;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.7

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019154 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))