Average Error: 29.3 → 0.2
Time: 20.7s
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 r6036690 = x;
        double r6036691 = 1.0;
        double r6036692 = r6036690 + r6036691;
        double r6036693 = sqrt(r6036692);
        double r6036694 = sqrt(r6036690);
        double r6036695 = r6036693 - r6036694;
        return r6036695;
}
↓
double f(double x) {
        double r6036696 = 1.0;
        double r6036697 = x;
        double r6036698 = r6036697 + r6036696;
        double r6036699 = sqrt(r6036698);
        double r6036700 = sqrt(r6036697);
        double r6036701 = r6036699 + r6036700;
        double r6036702 = r6036696 / r6036701;
        return r6036702;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.3
Target0.2
Herbie0.2
\[\frac{1}{\sqrt{x + 1} + \sqrt{x}}\]

Derivation

  1. Initial program 29.3

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

  3. Applied flip--29.1

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

  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 2019158 
(FPCore (x)
  :name "2sqrt (example 3.1)"

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

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