Average Error: 4.5 → 0.0
Time: 19.1s
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 r727038 = 2.0;
        double r727039 = x;
        double r727040 = r727038 * r727039;
        double r727041 = exp(r727040);
        double r727042 = 1.0;
        double r727043 = r727041 - r727042;
        double r727044 = exp(r727039);
        double r727045 = r727044 - r727042;
        double r727046 = r727043 / r727045;
        double r727047 = sqrt(r727046);
        return r727047;
}
↓
double f(double x) {
        double r727048 = x;
        double r727049 = exp(r727048);
        double r727050 = 1.0;
        double r727051 = r727049 + r727050;
        double r727052 = sqrt(r727051);
        return r727052;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.5

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))