Average Error: 0.0 → 0.0
Time: 5.9s
Precision: 64
Internal Precision: 576
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{-1} \cdot \left({\left(\sqrt{e^{x}}\right)}^{x} \cdot {\left(\sqrt{e^{x}}\right)}^{x}\right)\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Initial simplification0.0

    \[\leadsto e^{(x \cdot x + -1)_*}\]
  3. Using strategy rm

  4. Applied fma-udef0.0

    \[\leadsto e^{\color{blue}{x \cdot x + -1}}\]

  5. Applied exp-sum0.0

    \[\leadsto \color{blue}{e^{x \cdot x} \cdot e^{-1}}\]
  6. Using strategy rm

  7. Applied exp-prod0.0

    \[\leadsto \color{blue}{{\left(e^{x}\right)}^{x}} \cdot e^{-1}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt0.0

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

  10. Applied unpow-prod-down0.0

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

  11. Final simplification0.0

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

Runtime

Time bar (total: 5.9s)Debug logProfile

herbie shell --seed 2018248 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))