Average Error: 4.5 → 0.1
Time: 30.0s
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 r717451 = 2.0;
        double r717452 = x;
        double r717453 = r717451 * r717452;
        double r717454 = exp(r717453);
        double r717455 = 1.0;
        double r717456 = r717454 - r717455;
        double r717457 = exp(r717452);
        double r717458 = r717457 - r717455;
        double r717459 = r717456 / r717458;
        double r717460 = sqrt(r717459);
        return r717460;
}
↓
double f(double x) {
        double r717461 = x;
        double r717462 = exp(r717461);
        double r717463 = 1.0;
        double r717464 = r717462 + r717463;
        double r717465 = sqrt(r717464);
        return r717465;
}

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. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))