(/ 1 (sqrt (+ 1 (* (* (- alphax) alphax) (log (- 1 u))))))

Average Error: 11.0 → 11.0

Time: 2.7s

Precision: binary64

Math

\[\frac{1}{\sqrt{1 + \left(\left(-alphax\right) \cdot alphax\right) \cdot \log \left(1 - u\right)}}\]

↓

\[\frac{1}{\sqrt{1 + \left(\left(-alphax\right) \cdot alphax\right) \cdot \log \left(1 - u\right)}}\]

Error

Bits error versus alphax

Bits error versus u

Derivation

1. Initial program 11.0

   \[\frac{1}{\sqrt{1 + \left(\left(-alphax\right) \cdot alphax\right) \cdot \log \left(1 - u\right)}}\]

2. Final simplification 11.0

   \[\leadsto \frac{1}{\sqrt{1 + \left(\left(-alphax\right) \cdot alphax\right) \cdot \log \left(1 - u\right)}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (alphax u)
  :name "(/ 1 (sqrt (+ 1 (* (* (- alphax) alphax) (log (- 1 u))))))"
  :precision binary64
  (/ 1.0 (sqrt (+ 1.0 (* (* (neg alphax) alphax) (log (- 1.0 u)))))))