Average Error: 4.4 → 0.1
Time: 25.9s
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 r1087411 = 2.0;
        double r1087412 = x;
        double r1087413 = r1087411 * r1087412;
        double r1087414 = exp(r1087413);
        double r1087415 = 1.0;
        double r1087416 = r1087414 - r1087415;
        double r1087417 = exp(r1087412);
        double r1087418 = r1087417 - r1087415;
        double r1087419 = r1087416 / r1087418;
        double r1087420 = sqrt(r1087419);
        return r1087420;
}
↓
double f(double x) {
        double r1087421 = x;
        double r1087422 = exp(r1087421);
        double r1087423 = 1.0;
        double r1087424 = r1087422 + r1087423;
        double r1087425 = sqrt(r1087424);
        return r1087425;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.4

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))