Average Error: 13.8 → 0.1
Time: 1.2min
Precision: binary64
Cost: 448
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{x}}{x + 1}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{x}}{x + 1}
(FPCore (x) :precision binary64 (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))
↓
(FPCore (x) :precision binary64 (/ (/ -1.0 x) (+ x 1.0)))
double code(double x) {
	return (1.0 / (x + 1.0)) - (1.0 / x);
}
↓
double code(double x) {
	return (-1.0 / x) / (x + 1.0);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.4
Cost448
\[\frac{-1}{x \cdot \left(x + 1\right)}\]
Alternative 2
Error1.0
Cost648
\[\begin{array}{l} \mathbf{if}\;x \leq -0.997833285118038 \lor \neg \left(x \leq 0.760435366289126\right):\\ \;\;\;\;\frac{\frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{x} + 1\\ \end{array}\]
Alternative 3
Error1.3
Cost648
\[\begin{array}{l} \mathbf{if}\;x \leq -0.997833285118038 \lor \neg \left(x \leq 0.9986407271357947\right):\\ \;\;\;\;\frac{\frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{x}\\ \end{array}\]
Alternative 4
Error15.2
Cost834
\[\begin{array}{l} \mathbf{if}\;x \leq -0.997833285118038:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 4.475504231519108 \cdot 10^{+102}:\\ \;\;\;\;\frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 5
Error46.4
Cost64
\[0\]
Alternative 6
Error61.6
Cost64
\[-1\]

Error

Derivation

  1. Initial program 13.8

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

  3. Applied frac-sub_binary64_42813.2

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

  4. Simplified0.4

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

  5. Simplified0.4

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

  7. Applied associate-/r*_binary64_3630.1

    \[\leadsto \color{blue}{\frac{\frac{-1}{x}}{1 + x}}\]
  8. Using strategy rm

  9. Applied *-un-lft-identity_binary64_4190.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2021014 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))