Average Error: 4.3 → 0.1
Time: 22.1s
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 r1087875 = 2.0;
        double r1087876 = x;
        double r1087877 = r1087875 * r1087876;
        double r1087878 = exp(r1087877);
        double r1087879 = 1.0;
        double r1087880 = r1087878 - r1087879;
        double r1087881 = exp(r1087876);
        double r1087882 = r1087881 - r1087879;
        double r1087883 = r1087880 / r1087882;
        double r1087884 = sqrt(r1087883);
        return r1087884;
}
↓
double f(double x) {
        double r1087885 = x;
        double r1087886 = exp(r1087885);
        double r1087887 = 1.0;
        double r1087888 = r1087886 + r1087887;
        double r1087889 = sqrt(r1087888);
        return r1087889;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))