(atan (sqrt (* (* (- a) a) (log x))))

Average Error: 14.5 → 14.5

Time: 2.4s

Precision: binary64

Math

\[\tan^{-1} \left(\sqrt{\left(\left(-a\right) \cdot a\right) \cdot \log x}\right)\]

↓

\[\tan^{-1} \left(\sqrt{\left(\left(-a\right) \cdot a\right) \cdot \log x}\right)\]

Error

Bits error versus a

Bits error versus x

Derivation

1. Initial program 14.5

   \[\tan^{-1} \left(\sqrt{\left(\left(-a\right) \cdot a\right) \cdot \log x}\right)\]

2. Final simplification 14.5

   \[\leadsto \tan^{-1} \left(\sqrt{\left(\left(-a\right) \cdot a\right) \cdot \log x}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a x)
  :name "(atan (sqrt (* (* (- a) a) (log x))))"
  :precision binary64
  (atan (sqrt (* (* (neg a) a) (log x)))))