Average Error: 4.4 → 0.0
Time: 19.8s
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 r446260 = 2.0;
        double r446261 = x;
        double r446262 = r446260 * r446261;
        double r446263 = exp(r446262);
        double r446264 = 1.0;
        double r446265 = r446263 - r446264;
        double r446266 = exp(r446261);
        double r446267 = r446266 - r446264;
        double r446268 = r446265 / r446267;
        double r446269 = sqrt(r446268);
        return r446269;
}
↓
double f(double x) {
        double r446270 = x;
        double r446271 = exp(r446270);
        double r446272 = 1.0;
        double r446273 = r446271 + r446272;
        double r446274 = sqrt(r446273);
        return r446274;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019151 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))