Average Error: 14.2 → 0.1
Time: 2.8s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{1}{x + 1} \cdot \frac{0 - 1}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{1}{x + 1} \cdot \frac{0 - 1}{x}
double f(double x) {
        double r25107 = 1.0;
        double r25108 = x;
        double r25109 = r25108 + r25107;
        double r25110 = r25107 / r25109;
        double r25111 = r25107 / r25108;
        double r25112 = r25110 - r25111;
        return r25112;
}
↓
double f(double x) {
        double r25113 = 1.0;
        double r25114 = x;
        double r25115 = r25114 + r25113;
        double r25116 = r25113 / r25115;
        double r25117 = 0.0;
        double r25118 = r25117 - r25113;
        double r25119 = r25118 / r25114;
        double r25120 = r25116 * r25119;
        return r25120;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.2

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

  3. Applied frac-sub13.6

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

  4. Simplified13.6

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

  6. Applied times-frac13.6

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))