Average Error: 4.3 → 0.2
Time: 19.5s
Precision: 64
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
↓
\[\sqrt{\frac{{\left(e^{x}\right)}^{3} + 1}{e^{x} \cdot e^{x} + \left(1 - e^{x}\right)}}\]
\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}
↓
\sqrt{\frac{{\left(e^{x}\right)}^{3} + 1}{e^{x} \cdot e^{x} + \left(1 - e^{x}\right)}}
double f(double x) {
        double r340863 = 2.0;
        double r340864 = x;
        double r340865 = r340863 * r340864;
        double r340866 = exp(r340865);
        double r340867 = 1.0;
        double r340868 = r340866 - r340867;
        double r340869 = exp(r340864);
        double r340870 = r340869 - r340867;
        double r340871 = r340868 / r340870;
        double r340872 = sqrt(r340871);
        return r340872;
}
↓
double f(double x) {
        double r340873 = x;
        double r340874 = exp(r340873);
        double r340875 = 3.0;
        double r340876 = pow(r340874, r340875);
        double r340877 = 1.0;
        double r340878 = r340876 + r340877;
        double r340879 = r340874 * r340874;
        double r340880 = r340877 - r340874;
        double r340881 = r340879 + r340880;
        double r340882 = r340878 / r340881;
        double r340883 = sqrt(r340882);
        return r340883;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.3

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

  2. Simplified0.1

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

  4. Applied flip3-+0.2

    \[\leadsto \sqrt{\color{blue}{\frac{{\left(e^{x}\right)}^{3} + {1}^{3}}{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}}\]

  5. Final simplification0.2

    \[\leadsto \sqrt{\frac{{\left(e^{x}\right)}^{3} + 1}{e^{x} \cdot e^{x} + \left(1 - e^{x}\right)}}\]

Reproduce

herbie shell --seed 2019112 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))