Average Error: 29.5 → 0.2
Time: 1.0m
Precision: 64
\[\sqrt{x + 1} - \sqrt{x}\]
↓
\[\frac{\left(x - x\right) + 1}{\sqrt{1 + x} + \sqrt{x}}\]
\sqrt{x + 1} - \sqrt{x}
↓
\frac{\left(x - x\right) + 1}{\sqrt{1 + x} + \sqrt{x}}
double f(double x) {
        double r23340728 = x;
        double r23340729 = 1.0;
        double r23340730 = r23340728 + r23340729;
        double r23340731 = sqrt(r23340730);
        double r23340732 = sqrt(r23340728);
        double r23340733 = r23340731 - r23340732;
        return r23340733;
}
↓
double f(double x) {
        double r23340734 = x;
        double r23340735 = r23340734 - r23340734;
        double r23340736 = 1.0;
        double r23340737 = r23340735 + r23340736;
        double r23340738 = r23340736 + r23340734;
        double r23340739 = sqrt(r23340738);
        double r23340740 = sqrt(r23340734);
        double r23340741 = r23340739 + r23340740;
        double r23340742 = r23340737 / r23340741;
        return r23340742;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.5
Target0.2
Herbie0.2
\[\frac{1}{\sqrt{x + 1} + \sqrt{x}}\]

Derivation

  1. Initial program 29.5

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

  3. Applied flip--29.4

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

  4. Simplified0.2

    \[\leadsto \frac{\color{blue}{1 + \left(x - x\right)}}{\sqrt{x + 1} + \sqrt{x}}\]

  5. Final simplification0.2

    \[\leadsto \frac{\left(x - x\right) + 1}{\sqrt{1 + x} + \sqrt{x}}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "Main:bigenough3 from C"

  :herbie-target
  (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

  (- (sqrt (+ x 1.0)) (sqrt x)))