Average Error: 4.5 → 0.1
Time: 28.8s
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 r694654 = 2.0;
        double r694655 = x;
        double r694656 = r694654 * r694655;
        double r694657 = exp(r694656);
        double r694658 = 1.0;
        double r694659 = r694657 - r694658;
        double r694660 = exp(r694655);
        double r694661 = r694660 - r694658;
        double r694662 = r694659 / r694661;
        double r694663 = sqrt(r694662);
        return r694663;
}
↓
double f(double x) {
        double r694664 = x;
        double r694665 = exp(r694664);
        double r694666 = 1.0;
        double r694667 = r694665 + r694666;
        double r694668 = sqrt(r694667);
        return r694668;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.5

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019107 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))