Average Error: 4.3 → 0.1
Time: 19.9s
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 r434123 = 2.0;
        double r434124 = x;
        double r434125 = r434123 * r434124;
        double r434126 = exp(r434125);
        double r434127 = 1.0;
        double r434128 = r434126 - r434127;
        double r434129 = exp(r434124);
        double r434130 = r434129 - r434127;
        double r434131 = r434128 / r434130;
        double r434132 = sqrt(r434131);
        return r434132;
}
↓
double f(double x) {
        double r434133 = 1.0;
        double r434134 = x;
        double r434135 = exp(r434134);
        double r434136 = r434133 + r434135;
        double r434137 = sqrt(r434136);
        return r434137;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019142 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))