Average Error: 14.2 → 0.4
Time: 2.0s
Precision: binary64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{1}{x \cdot \left(-1 - x\right)}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{1}{x \cdot \left(-1 - x\right)}
(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 14.2

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

  3. Applied frac-sub_binary6413.5

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

  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 frac-2neg_binary640.4

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

  8. Simplified0.4

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

  9. Simplified0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2021173 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))