Average Error: 30.0 → 0.2
Time: 14.1s
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 r4120902 = x;
        double r4120903 = 1.0;
        double r4120904 = r4120902 + r4120903;
        double r4120905 = sqrt(r4120904);
        double r4120906 = sqrt(r4120902);
        double r4120907 = r4120905 - r4120906;
        return r4120907;
}
↓
double f(double x) {
        double r4120908 = 1.0;
        double r4120909 = x;
        double r4120910 = r4120909 + r4120908;
        double r4120911 = sqrt(r4120910);
        double r4120912 = sqrt(r4120909);
        double r4120913 = r4120911 + r4120912;
        double r4120914 = r4120908 / r4120913;
        return r4120914;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original30.0
Target0.2
Herbie0.2
\[\frac{1}{\sqrt{x + 1} + \sqrt{x}}\]

Derivation

  1. Initial program 30.0

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

  3. Applied flip--29.7

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

  4. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019137 
(FPCore (x)
  :name "2sqrt (example 3.1)"

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

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