Average Error: 0.1 → 0.1
Time: 11.9s
Precision: 64
\[\frac{1}{\sqrt{1 + x}}\]
\[\frac{1}{\sqrt{1 + x}}\]
\frac{1}{\sqrt{1 + x}}
\frac{1}{\sqrt{1 + x}}
double f(double x) {
        double r1682973 = 1.0;
        double r1682974 = x;
        double r1682975 = r1682973 + r1682974;
        double r1682976 = sqrt(r1682975);
        double r1682977 = r1682973 / r1682976;
        return r1682977;
}

double f(double x) {
        double r1682978 = 1.0;
        double r1682979 = x;
        double r1682980 = r1682978 + r1682979;
        double r1682981 = sqrt(r1682980);
        double r1682982 = r1682978 / r1682981;
        return r1682982;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{1}{\sqrt{1 + x}}\]
  2. Final simplification0.1

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

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "1/sqrt(1+x)"
  :precision binary64
  (/ 1 (sqrt (+ 1 x))))