Average Error: 4.5 → 0.0
Time: 16.1s
Precision: 64
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
↓
\[\sqrt{1 + e^{x}}\]
\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}
↓
\sqrt{1 + e^{x}}
double f(double x) {
        double r586851 = 2.0;
        double r586852 = x;
        double r586853 = r586851 * r586852;
        double r586854 = exp(r586853);
        double r586855 = 1.0;
        double r586856 = r586854 - r586855;
        double r586857 = exp(r586852);
        double r586858 = r586857 - r586855;
        double r586859 = r586856 / r586858;
        double r586860 = sqrt(r586859);
        return r586860;
}
↓
double f(double x) {
        double r586861 = 1.0;
        double r586862 = x;
        double r586863 = exp(r586862);
        double r586864 = r586861 + r586863;
        double r586865 = sqrt(r586864);
        return r586865;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.5

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

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