Average Error: 14.3 → 0.1
Time: 13.3s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{1 + x}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{1 + x}}{x}
double f(double x) {
        double r3958410 = 1.0;
        double r3958411 = x;
        double r3958412 = r3958411 + r3958410;
        double r3958413 = r3958410 / r3958412;
        double r3958414 = r3958410 / r3958411;
        double r3958415 = r3958413 - r3958414;
        return r3958415;
}
↓
double f(double x) {
        double r3958416 = 1.0;
        double r3958417 = -r3958416;
        double r3958418 = x;
        double r3958419 = r3958416 + r3958418;
        double r3958420 = r3958417 / r3958419;
        double r3958421 = r3958420 / r3958418;
        return r3958421;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.3

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

  3. Applied frac-sub13.7

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

  4. Taylor expanded around 0 0.4

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))