(- x (/ (sqrt x) (* (/ 1 2) (pow x (/ (- 1) 2)))))

Average Error: 0.5 → 0.5

Time: 1.6s

Precision: binary64

Math

\[x - \frac{\sqrt{x}}{\frac{1}{2} \cdot {x}^{\left(\frac{-1}{2}\right)}}\]

↓

\[x - \frac{\sqrt{x}}{\frac{1}{2} \cdot {x}^{\left(\frac{-1}{2}\right)}}\]

Error

Bits error versus x

Derivation

1. Initial program 0.5

   \[x - \frac{\sqrt{x}}{\frac{1}{2} \cdot {x}^{\left(\frac{-1}{2}\right)}}\]

2. Final simplification 0.5

   \[\leadsto x - \frac{\sqrt{x}}{\frac{1}{2} \cdot {x}^{\left(\frac{-1}{2}\right)}}\]

Reproduce

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