Average Error: 30.0 → 0.2
Time: 17.7s
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 r5486077 = x;
        double r5486078 = 1.0;
        double r5486079 = r5486077 + r5486078;
        double r5486080 = sqrt(r5486079);
        double r5486081 = sqrt(r5486077);
        double r5486082 = r5486080 - r5486081;
        return r5486082;
}
↓
double f(double x) {
        double r5486083 = 1.0;
        double r5486084 = x;
        double r5486085 = r5486084 + r5486083;
        double r5486086 = sqrt(r5486085);
        double r5486087 = sqrt(r5486084);
        double r5486088 = r5486086 + r5486087;
        double r5486089 = r5486083 / r5486088;
        return r5486089;
}

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--29.9

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

  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 2019168 
(FPCore (x)
  :name "2sqrt (example 3.1)"

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

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