Average Error: 4.4 → 0.1
Time: 20.1s
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 r660948 = 2.0;
        double r660949 = x;
        double r660950 = r660948 * r660949;
        double r660951 = exp(r660950);
        double r660952 = 1.0;
        double r660953 = r660951 - r660952;
        double r660954 = exp(r660949);
        double r660955 = r660954 - r660952;
        double r660956 = r660953 / r660955;
        double r660957 = sqrt(r660956);
        return r660957;
}
↓
double f(double x) {
        double r660958 = 1.0;
        double r660959 = x;
        double r660960 = exp(r660959);
        double r660961 = r660958 + r660960;
        double r660962 = sqrt(r660961);
        return r660962;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019152 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))