Average Error: 14.5 → 0.1
Time: 5.7s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{\left(\frac{x}{1} \cdot 1 - x\right) - 1}{\frac{x}{1}}}{x + 1}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{\left(\frac{x}{1} \cdot 1 - x\right) - 1}{\frac{x}{1}}}{x + 1}
double code(double x) {
	return ((double) (((double) (1.0 / ((double) (x + 1.0)))) - ((double) (1.0 / x))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (x / 1.0)) * 1.0)) - x)) - 1.0)) / ((double) (x / 1.0)))) / ((double) (x + 1.0))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

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

  3. Applied clear-num14.5

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

  4. Applied frac-sub13.9

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

  5. Simplified0.4

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

  7. Applied *-commutative0.4

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

  8. Applied associate-/r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020114 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))