Average Error: 14.9 → 0.1
Time: 25.3s
Precision: 64
\[\frac{1.0}{x + 1.0} - \frac{1.0}{x}\]
↓
\[\frac{\frac{-1.0}{1.0 + x}}{x}\]
\frac{1.0}{x + 1.0} - \frac{1.0}{x}
↓
\frac{\frac{-1.0}{1.0 + x}}{x}
double f(double x) {
        double r4007777 = 1.0;
        double r4007778 = x;
        double r4007779 = r4007778 + r4007777;
        double r4007780 = r4007777 / r4007779;
        double r4007781 = r4007777 / r4007778;
        double r4007782 = r4007780 - r4007781;
        return r4007782;
}
↓
double f(double x) {
        double r4007783 = 1.0;
        double r4007784 = -r4007783;
        double r4007785 = x;
        double r4007786 = r4007783 + r4007785;
        double r4007787 = r4007784 / r4007786;
        double r4007788 = r4007787 / r4007785;
        return r4007788;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.9

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

  3. Applied frac-sub14.3

    \[\leadsto \color{blue}{\frac{1.0 \cdot x - \left(x + 1.0\right) \cdot 1.0}{\left(x + 1.0\right) \cdot x}}\]

  4. Taylor expanded around 0 0.4

    \[\leadsto \frac{\color{blue}{-1.0}}{\left(x + 1.0\right) \cdot x}\]
  5. Using strategy rm

  6. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{-1.0}{x + 1.0}}{x}}\]

  7. Final simplification0.1

    \[\leadsto \frac{\frac{-1.0}{1.0 + x}}{x}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))