(- (* y (exp (* (/ (- 1) l) x))) (/ y E))

Average Error: 0.3 → 0.3

Time: 1.4s

Precision: binary64

Math

\[y \cdot e^{\frac{-1}{\ell} \cdot x} - \frac{y}{e}\]

↓

\[y \cdot e^{\frac{-1}{\ell} \cdot x} - \frac{y}{e}\]

Error

Bits error versus y

Bits error versus l

Bits error versus x

Derivation

1. Initial program 0.3

   \[y \cdot e^{\frac{-1}{\ell} \cdot x} - \frac{y}{e}\]

2. Final simplification 0.3

   \[\leadsto y \cdot e^{\frac{-1}{\ell} \cdot x} - \frac{y}{e}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (y l x)
  :name "(- (* y (exp (* (/ (- 1) l) x))) (/ y E))"
  :precision binary64
  (- (* y (exp (* (/ (neg 1.0) l) x))) (/ y E)))