Average Error: 14.8 → 0.1
Time: 13.7s
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 r33102 = 1.0;
        double r33103 = x;
        double r33104 = r33103 + r33102;
        double r33105 = r33102 / r33104;
        double r33106 = r33102 / r33103;
        double r33107 = r33105 - r33106;
        return r33107;
}
↓
double f(double x) {
        double r33108 = 1.0;
        double r33109 = -r33108;
        double r33110 = r33109 * r33108;
        double r33111 = x;
        double r33112 = r33111 + r33108;
        double r33113 = r33110 / r33112;
        double r33114 = r33113 / r33111;
        return r33114;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  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. Simplified14.1

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

  6. Applied associate-/r*14.1

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

  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 2019198 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))