exp neg sub

Average Error: 0.0 → 0.0

Time: 2.0s

Precision: 64

Math

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

↓

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

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[e^{-\left(1 - x \cdot x\right)}\]
2. Using strategy rm

3. Applied *-un-lft-identity 0.0

   \[\leadsto e^{\color{blue}{1 \cdot \left(-\left(1 - x \cdot x\right)\right)}}\]

4. Applied exp-prod 0.0

   \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left(-\left(1 - x \cdot x\right)\right)}}\]

5. Simplified 0.0

   \[\leadsto {\color{blue}{e}}^{\left(-\left(1 - x \cdot x\right)\right)}\]

6. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020126 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))