Average Error: 14.3 → 0.1
Time: 1.5s
Precision: binary64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\left(-1\right) \cdot \frac{1}{x}}{1 + x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\left(-1\right) \cdot \frac{1}{x}}{1 + x}
(FPCore (x) :precision binary64 (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))
↓
(FPCore (x) :precision binary64 (/ (* (- 1.0) (/ 1.0 x)) (+ 1.0 x)))
double code(double x) {
	return ((double) ((1.0 / ((double) (x + 1.0))) - (1.0 / x)));
}
↓
double code(double x) {
	return (((double) (((double) -(1.0)) * (1.0 / x))) / ((double) (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 14.3

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

  3. Applied frac-sub_binary6413.7

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

  4. Simplified0.4

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

  5. Simplified0.4

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

  7. Applied associate-/r*_binary640.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020210 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))