Average Error: 4.0 → 0.1
Time: 21.5s
Precision: 64
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
↓
\[\sqrt{\sqrt{1 + e^{x}}} \cdot \sqrt{\sqrt{1 + e^{x}}}\]
\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}
↓
\sqrt{\sqrt{1 + e^{x}}} \cdot \sqrt{\sqrt{1 + e^{x}}}
double f(double x) {
        double r486980 = 2.0;
        double r486981 = x;
        double r486982 = r486980 * r486981;
        double r486983 = exp(r486982);
        double r486984 = 1.0;
        double r486985 = r486983 - r486984;
        double r486986 = exp(r486981);
        double r486987 = r486986 - r486984;
        double r486988 = r486985 / r486987;
        double r486989 = sqrt(r486988);
        return r486989;
}
↓
double f(double x) {
        double r486990 = 1.0;
        double r486991 = x;
        double r486992 = exp(r486991);
        double r486993 = r486990 + r486992;
        double r486994 = sqrt(r486993);
        double r486995 = sqrt(r486994);
        double r486996 = r486995 * r486995;
        return r486996;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\sqrt{1 + e^{x}}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019144 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))