Average Error: 4.1 → 0.1
Time: 21.5s
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 r632032 = 2.0;
        double r632033 = x;
        double r632034 = r632032 * r632033;
        double r632035 = exp(r632034);
        double r632036 = 1.0;
        double r632037 = r632035 - r632036;
        double r632038 = exp(r632033);
        double r632039 = r632038 - r632036;
        double r632040 = r632037 / r632039;
        double r632041 = sqrt(r632040);
        return r632041;
}
↓
double f(double x) {
        double r632042 = x;
        double r632043 = exp(r632042);
        double r632044 = 1.0;
        double r632045 = r632043 + r632044;
        double r632046 = sqrt(r632045);
        return r632046;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019141 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))