Average Error: 14.7 → 0.1
Time: 25.2s
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 r2480410 = 1.0;
        double r2480411 = x;
        double r2480412 = r2480411 + r2480410;
        double r2480413 = r2480410 / r2480412;
        double r2480414 = r2480410 / r2480411;
        double r2480415 = r2480413 - r2480414;
        return r2480415;
}
↓
double f(double x) {
        double r2480416 = 1.0;
        double r2480417 = -r2480416;
        double r2480418 = x;
        double r2480419 = r2480416 + r2480418;
        double r2480420 = r2480417 / r2480419;
        double r2480421 = r2480420 / r2480418;
        return r2480421;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

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

  3. Applied frac-sub14.1

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

  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 2019168 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))