(pow (pow x (/ (- 1) 2)) 3)

Average Error: 0.6 → 0.6

Time: 2.0s

Precision: binary64

Math

\[{\left({x}^{\left(\frac{-1}{2}\right)}\right)}^{3}\]

↓

\[{\left({x}^{\left(\frac{-1}{2}\right)}\right)}^{3}\]

Error

Bits error versus x

Derivation

1. Initial program 0.6

   \[{\left({x}^{\left(\frac{-1}{2}\right)}\right)}^{3}\]

2. Final simplification 0.6

   \[\leadsto {\left({x}^{\left(\frac{-1}{2}\right)}\right)}^{3}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(pow (pow x (/ (- 1) 2)) 3)"
  :precision binary64
  (pow (pow x (/ (neg 1.0) 2.0)) 3.0))