(/ (log (+ x (pow x (- y)))) (log x))

Average Error: 19.4 → 19.4

Time: 3.2s

Precision: binary64

Math

\[\frac{\log \left(x + {x}^{\left(-y\right)}\right)}{\log x}\]

↓

\[\frac{\log \left(x + {x}^{\left(-y\right)}\right)}{\log x}\]

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 19.4

   \[\frac{\log \left(x + {x}^{\left(-y\right)}\right)}{\log x}\]

2. Final simplification 19.4

   \[\leadsto \frac{\log \left(x + {x}^{\left(-y\right)}\right)}{\log x}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(/ (log (+ x (pow x (- y)))) (log x))"
  :precision binary64
  (/ (log (+ x (pow x (neg y)))) (log x)))