Average Error: 30.0 → 0.2
Time: 18.0s
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 r3454905 = x;
        double r3454906 = 1.0;
        double r3454907 = r3454905 + r3454906;
        double r3454908 = sqrt(r3454907);
        double r3454909 = sqrt(r3454905);
        double r3454910 = r3454908 - r3454909;
        return r3454910;
}
↓
double f(double x) {
        double r3454911 = 1.0;
        double r3454912 = x;
        double r3454913 = r3454912 + r3454911;
        double r3454914 = sqrt(r3454913);
        double r3454915 = sqrt(r3454912);
        double r3454916 = r3454914 + r3454915;
        double r3454917 = r3454911 / r3454916;
        return r3454917;
}

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--29.8

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

  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 2019132 
(FPCore (x)
  :name "2sqrt (example 3.1)"

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

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