Average Error: 4.2 → 0.1
Time: 42.6s
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 r1326084 = 2.0;
        double r1326085 = x;
        double r1326086 = r1326084 * r1326085;
        double r1326087 = exp(r1326086);
        double r1326088 = 1.0;
        double r1326089 = r1326087 - r1326088;
        double r1326090 = exp(r1326085);
        double r1326091 = r1326090 - r1326088;
        double r1326092 = r1326089 / r1326091;
        double r1326093 = sqrt(r1326092);
        return r1326093;
}
↓
double f(double x) {
        double r1326094 = x;
        double r1326095 = exp(r1326094);
        double r1326096 = 1.0;
        double r1326097 = r1326095 + r1326096;
        double r1326098 = sqrt(r1326097);
        return r1326098;
}

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 2019120 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))