(- (- x (/ (- (pow x n) k) (* n (pow x (- n 1))))) (- timeout))

Average Error: 1.6 → 1.6

Time: 14.8s

Precision: binary64

Math

\[\left(x - \frac{{x}^{n} - k}{n \cdot {x}^{\left(n - 1\right)}}\right) - \left(-timeout\right)\]

↓

\[x - \left(\frac{{x}^{n} - k}{n \cdot {x}^{\left(n - 1\right)}} - timeout\right)\]

Error

Bits error versus x

Bits error versus n

Bits error versus k

Bits error versus timeout

Derivation

1. Initial program 1.6

   \[\left(x - \frac{{x}^{n} - k}{n \cdot {x}^{\left(n - 1\right)}}\right) - \left(-timeout\right)\]

2. Simplified 1.6

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

3. Final simplification 1.6

   \[\leadsto x - \left(\frac{{x}^{n} - k}{n \cdot {x}^{\left(n - 1\right)}} - timeout\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x n k timeout)
  :name "(- (- x (/ (- (pow x n) k) (* n (pow x (- n 1))))) (- timeout))"
  :precision binary64
  (- (- x (/ (- (pow x n) k) (* n (pow x (- n 1.0))))) (neg timeout)))