Average Error: 4.4 → 0.1
Time: 21.8s
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 r406170 = 2.0;
        double r406171 = x;
        double r406172 = r406170 * r406171;
        double r406173 = exp(r406172);
        double r406174 = 1.0;
        double r406175 = r406173 - r406174;
        double r406176 = exp(r406171);
        double r406177 = r406176 - r406174;
        double r406178 = r406175 / r406177;
        double r406179 = sqrt(r406178);
        return r406179;
}
↓
double f(double x) {
        double r406180 = x;
        double r406181 = exp(r406180);
        double r406182 = 1.0;
        double r406183 = r406181 + r406182;
        double r406184 = sqrt(r406183);
        return r406184;
}

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

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

  3. Final simplification0.1

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

Reproduce

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