Average Error: 14.5 → 0.1
Time: 10.2s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{\frac{x + 1}{1}}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{\frac{x + 1}{1}}}{x}
double f(double x) {
        double r54045 = 1.0;
        double r54046 = x;
        double r54047 = r54046 + r54045;
        double r54048 = r54045 / r54047;
        double r54049 = r54045 / r54046;
        double r54050 = r54048 - r54049;
        return r54050;
}
↓
double f(double x) {
        double r54051 = 1.0;
        double r54052 = -r54051;
        double r54053 = x;
        double r54054 = r54053 + r54051;
        double r54055 = r54054 / r54051;
        double r54056 = r54052 / r54055;
        double r54057 = r54056 / r54053;
        return r54057;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

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

  3. Applied frac-sub13.9

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

  4. Simplified13.9

    \[\leadsto \frac{\color{blue}{1 \cdot \left(x - \left(x + 1\right)\right)}}{\left(x + 1\right) \cdot x}\]
  5. Using strategy rm

  6. Applied associate-/r*13.9

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

  7. Simplified0.1

    \[\leadsto \frac{\color{blue}{\frac{-1}{\frac{x + 1}{1}}}}{x}\]

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))