Average Error: 14.4 → 0.1
Time: 13.4s
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 r1318108 = 1.0;
        double r1318109 = x;
        double r1318110 = r1318109 + r1318108;
        double r1318111 = r1318108 / r1318110;
        double r1318112 = r1318108 / r1318109;
        double r1318113 = r1318111 - r1318112;
        return r1318113;
}
↓
double f(double x) {
        double r1318114 = -1.0;
        double r1318115 = x;
        double r1318116 = 1.0;
        double r1318117 = r1318115 + r1318116;
        double r1318118 = r1318114 / r1318117;
        double r1318119 = r1318118 / r1318115;
        return r1318119;
}

Error

Bits error versus x

Try it out

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-sub13.8

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

  4. Simplified0.4

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

  5. Simplified0.4

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

  7. Applied distribute-rgt1-in0.4

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

  8. Applied associate-/r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019137 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))