Average Error: 14.3 → 0.3
Time: 8.8s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{1}{\frac{x + 1}{1} \cdot \frac{x}{-1}}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{1}{\frac{x + 1}{1} \cdot \frac{x}{-1}}
double f(double x) {
        double r32165 = 1.0;
        double r32166 = x;
        double r32167 = r32166 + r32165;
        double r32168 = r32165 / r32167;
        double r32169 = r32165 / r32166;
        double r32170 = r32168 - r32169;
        return r32170;
}
↓
double f(double x) {
        double r32171 = 1.0;
        double r32172 = x;
        double r32173 = 1.0;
        double r32174 = r32172 + r32173;
        double r32175 = r32174 / r32173;
        double r32176 = -r32173;
        double r32177 = r32172 / r32176;
        double r32178 = r32175 * r32177;
        double r32179 = r32171 / r32178;
        return r32179;
}

Error

Bits error versus x

Try it out

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. Simplified13.7

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

  5. Simplified13.7

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

  7. Applied clear-num13.7

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

  8. Simplified0.3

    \[\leadsto \frac{1}{\color{blue}{\frac{x}{0 - 1} \cdot \frac{1 + x}{1}}}\]

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))