Average Error: 14.4 → 0.1
Time: 17.9s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{\left(-1\right) \cdot 1}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{\left(-1\right) \cdot 1}{x + 1}}{x}
double f(double x) {
        double r22297 = 1.0;
        double r22298 = x;
        double r22299 = r22298 + r22297;
        double r22300 = r22297 / r22299;
        double r22301 = r22297 / r22298;
        double r22302 = r22300 - r22301;
        return r22302;
}
↓
double f(double x) {
        double r22303 = 1.0;
        double r22304 = -r22303;
        double r22305 = r22304 * r22303;
        double r22306 = x;
        double r22307 = r22306 + r22303;
        double r22308 = r22305 / r22307;
        double r22309 = r22308 / r22306;
        return r22309;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.4

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  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. Simplified13.7

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

  6. Applied associate-/r*13.7

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))