(- (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))) (- timeout))

Average Error: 2.2 → 2.2

Time: 1.1s

Precision: binary64

Math

\[\left(\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\right) - \left(-timeout\right)\]

↓

\[\left(\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\right) - \left(-timeout\right)\]

Error

Bits error versus x

Bits error versus timeout

Derivation

1. Initial program 2.2

   \[\left(\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\right) - \left(-timeout\right)\]

2. Final simplification 2.2

   \[\leadsto \left(\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\right) - \left(-timeout\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x timeout)
  :name "(- (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))) (- timeout))"
  :precision binary64
  (- (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))) (neg timeout)))