Average Error: 29.9 → 0.2
Time: 16.9s
Precision: 64
\[\sqrt{x + 1} - \sqrt{x}\]
↓
\[\frac{1}{\sqrt{x + 1} + \sqrt{x}}\]
\sqrt{x + 1} - \sqrt{x}
↓
\frac{1}{\sqrt{x + 1} + \sqrt{x}}
double f(double x) {
        double r5101243 = x;
        double r5101244 = 1.0;
        double r5101245 = r5101243 + r5101244;
        double r5101246 = sqrt(r5101245);
        double r5101247 = sqrt(r5101243);
        double r5101248 = r5101246 - r5101247;
        return r5101248;
}
↓
double f(double x) {
        double r5101249 = 1.0;
        double r5101250 = x;
        double r5101251 = r5101250 + r5101249;
        double r5101252 = sqrt(r5101251);
        double r5101253 = sqrt(r5101250);
        double r5101254 = r5101252 + r5101253;
        double r5101255 = r5101249 / r5101254;
        return r5101255;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.9
Target0.2
Herbie0.2
\[\frac{1}{\sqrt{x + 1} + \sqrt{x}}\]

Derivation

  1. Initial program 29.9

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

  3. Applied flip--29.6

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

  4. Simplified0.2

    \[\leadsto \frac{\color{blue}{1 + 0}}{\sqrt{x + 1} + \sqrt{x}}\]

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "2sqrt (example 3.1)"

  :herbie-target
  (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

  (- (sqrt (+ x 1)) (sqrt x)))