Average Error: 0.2 → 0.2
Time: 3.2s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{x}{{\left(1 + \sqrt{x + 1}\right)}^{1}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{x}{{\left(1 + \sqrt{x + 1}\right)}^{1}}
double f(double x) {
        double r88182 = x;
        double r88183 = 1.0;
        double r88184 = r88182 + r88183;
        double r88185 = sqrt(r88184);
        double r88186 = r88183 + r88185;
        double r88187 = r88182 / r88186;
        return r88187;
}
↓
double f(double x) {
        double r88188 = x;
        double r88189 = 1.0;
        double r88190 = r88188 + r88189;
        double r88191 = sqrt(r88190);
        double r88192 = r88189 + r88191;
        double r88193 = 1.0;
        double r88194 = pow(r88192, r88193);
        double r88195 = r88188 / r88194;
        return r88195;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  3. Applied pow10.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))