Average Error: 0.2 → 0.2
Time: 12.9s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{x}{1 + \sqrt{1 + x}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{x}{1 + \sqrt{1 + x}}
double f(double x) {
        double r6803114 = x;
        double r6803115 = 1.0;
        double r6803116 = r6803114 + r6803115;
        double r6803117 = sqrt(r6803116);
        double r6803118 = r6803115 + r6803117;
        double r6803119 = r6803114 / r6803118;
        return r6803119;
}
↓
double f(double x) {
        double r6803120 = x;
        double r6803121 = 1.0;
        double r6803122 = r6803121 + r6803120;
        double r6803123 = sqrt(r6803122);
        double r6803124 = r6803121 + r6803123;
        double r6803125 = r6803120 / r6803124;
        return r6803125;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{x}{1 + \sqrt{x + 1}}\]
  2. Using strategy rm

  3. Applied +-commutative0.2

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

  4. Final simplification0.2

    \[\leadsto \frac{x}{1 + \sqrt{1 + x}}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))