Average Error: 0.2 → 0.2
Time: 15.7s
Precision: 64
\[\frac{x}{1.0 + \sqrt{x + 1.0}}\]
↓
\[x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}\]
\frac{x}{1.0 + \sqrt{x + 1.0}}
↓
x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}
double f(double x) {
        double r4840085 = x;
        double r4840086 = 1.0;
        double r4840087 = r4840085 + r4840086;
        double r4840088 = sqrt(r4840087);
        double r4840089 = r4840086 + r4840088;
        double r4840090 = r4840085 / r4840089;
        return r4840090;
}
↓
double f(double x) {
        double r4840091 = x;
        double r4840092 = 1.0;
        double r4840093 = 1.0;
        double r4840094 = r4840091 + r4840093;
        double r4840095 = sqrt(r4840094);
        double r4840096 = r4840093 + r4840095;
        double r4840097 = r4840092 / r4840096;
        double r4840098 = r4840091 * r4840097;
        return r4840098;
}

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

    \[\frac{x}{1.0 + \sqrt{x + 1.0}}\]
  2. Using strategy rm

  3. Applied div-inv0.2

    \[\leadsto \color{blue}{x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}}\]

  4. Final simplification0.2

    \[\leadsto x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))