Average Error: 14.5 → 0.1
Time: 3.2s
Precision: binary64
\[\frac{1}{x + 1} - \frac{1}{x} \]
↓
\[\frac{\frac{-1}{x + 1}}{x} \]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{x + 1}}{x}

(FPCore (x) :precision binary64 (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))
↓
(FPCore (x) :precision binary64 (/ (/ -1.0 (+ x 1.0)) x))
double code(double x) {
	return (1.0 / (x + 1.0)) - (1.0 / x);
}
↓
double code(double x) {
	return (-1.0 / (x + 1.0)) / x;
}

Error

Bits error versus x

Try it out

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. Applied frac-sub_binary6413.9

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

  3. Applied associate-/r*_binary6413.9

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2022004 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))