(exp (* alpha (- (- 1 x) 1)))

Average Error: 5.1 → 0.0

Time: 1.0s

Precision: binary64

Math

\[e^{\alpha \cdot \left(\left(1 - x\right) - 1\right)}\]

↓

\[e^{\left(-x\right) \cdot \alpha}\]

Error

Bits error versus alpha

Bits error versus x

Derivation

1. Initial program 5.1

   \[e^{\alpha \cdot \left(\left(1 - x\right) - 1\right)}\]

2. Simplified 0.0

   \[\leadsto \color{blue}{e^{\left(-x\right) \cdot \alpha}}\]

3. Final simplification 0.0

   \[\leadsto e^{\left(-x\right) \cdot \alpha}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (alpha x)
  :name "(exp (* alpha (- (- 1 x) 1)))"
  :precision binary64
  (exp (* alpha (- (- 1.0 x) 1.0))))