Average Error: 29.9 → 0.2
Time: 16.4s
Precision: 64
\[\sqrt{x + 1} - \sqrt{x}\]
↓
\[\frac{1}{\sqrt{1 + x} + \sqrt{x}}\]
\sqrt{x + 1} - \sqrt{x}
↓
\frac{1}{\sqrt{1 + x} + \sqrt{x}}
double f(double x) {
        double r4757946 = x;
        double r4757947 = 1.0;
        double r4757948 = r4757946 + r4757947;
        double r4757949 = sqrt(r4757948);
        double r4757950 = sqrt(r4757946);
        double r4757951 = r4757949 - r4757950;
        return r4757951;
}
↓
double f(double x) {
        double r4757952 = 1.0;
        double r4757953 = x;
        double r4757954 = r4757952 + r4757953;
        double r4757955 = sqrt(r4757954);
        double r4757956 = sqrt(r4757953);
        double r4757957 = r4757955 + r4757956;
        double r4757958 = r4757952 / r4757957;
        return r4757958;
}

Error

Bits error versus x

Try it out

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

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

  5. Final simplification0.2

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

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)))