Average Error: 14.7 → 0.1
Time: 22.5s
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 r3453523 = 1.0;
        double r3453524 = x;
        double r3453525 = r3453524 + r3453523;
        double r3453526 = r3453523 / r3453525;
        double r3453527 = r3453523 / r3453524;
        double r3453528 = r3453526 - r3453527;
        return r3453528;
}
↓
double f(double x) {
        double r3453529 = -1.0;
        double r3453530 = x;
        double r3453531 = r3453529 / r3453530;
        double r3453532 = 1.0;
        double r3453533 = r3453532 + r3453530;
        double r3453534 = r3453531 / r3453533;
        return r3453534;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

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

  3. Applied frac-sub14.0

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

  4. Simplified0.4

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

  5. Simplified0.4

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

  7. Applied *-un-lft-identity0.4

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

  8. Applied distribute-rgt-out0.4

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

  9. Applied associate-/r*0.1

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

  11. Applied *-un-lft-identity0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019120 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))