Average Error: 38.4 → 0.2
Time: 12.6s
Precision: 64
\[\sqrt{1 + x} - 1\]
\[\frac{x}{1 + \sqrt{x + 1}}\]
\sqrt{1 + x} - 1
\frac{x}{1 + \sqrt{x + 1}}
double f(double x) {
        double r45482422 = 1.0;
        double r45482423 = x;
        double r45482424 = r45482422 + r45482423;
        double r45482425 = sqrt(r45482424);
        double r45482426 = r45482425 - r45482422;
        return r45482426;
}

double f(double x) {
        double r45482427 = x;
        double r45482428 = 1.0;
        double r45482429 = r45482427 + r45482428;
        double r45482430 = sqrt(r45482429);
        double r45482431 = r45482428 + r45482430;
        double r45482432 = r45482427 / r45482431;
        return r45482432;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.4

    \[\sqrt{1 + x} - 1\]
  2. Using strategy rm
  3. Applied flip--38.5

    \[\leadsto \color{blue}{\frac{\sqrt{1 + x} \cdot \sqrt{1 + x} - 1 \cdot 1}{\sqrt{1 + x} + 1}}\]
  4. Simplified0.2

    \[\leadsto \frac{\color{blue}{x}}{\sqrt{1 + x} + 1}\]
  5. Final simplification0.2

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

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sqrt(1+x)-1"
  (- (sqrt (+ 1 x)) 1))