Average Error: 14.5 → 0.1
Time: 14.3s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{x + 1}}{x}
double f(double x) {
        double r1126389 = 1.0;
        double r1126390 = x;
        double r1126391 = r1126390 + r1126389;
        double r1126392 = r1126389 / r1126391;
        double r1126393 = r1126389 / r1126390;
        double r1126394 = r1126392 - r1126393;
        return r1126394;
}
↓
double f(double x) {
        double r1126395 = -1.0;
        double r1126396 = x;
        double r1126397 = 1.0;
        double r1126398 = r1126396 + r1126397;
        double r1126399 = r1126395 / r1126398;
        double r1126400 = r1126399 / r1126396;
        return r1126400;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

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

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

  5. Taylor expanded around 0 0.3

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

  7. Applied associate-/r*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))