Average Error: 14.7 → 0.1
Time: 1.5m
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{1}{x + 1} \cdot \left(-1\right)}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{1}{x + 1} \cdot \left(-1\right)}{x}
double f(double x) {
        double r32473 = 1.0;
        double r32474 = x;
        double r32475 = r32474 + r32473;
        double r32476 = r32473 / r32475;
        double r32477 = r32473 / r32474;
        double r32478 = r32476 - r32477;
        return r32478;
}
↓
double f(double x) {
        double r32479 = 1.0;
        double r32480 = x;
        double r32481 = r32480 + r32479;
        double r32482 = r32479 / r32481;
        double r32483 = -r32479;
        double r32484 = r32482 * r32483;
        double r32485 = r32484 / r32480;
        return r32485;
}

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-sub14.1

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

  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

    \[\leadsto \frac{\color{blue}{\frac{1}{x + 1} \cdot \left(0 - 1\right)}}{x}\]

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))