Average Error: 0.0 → 0.0
Time: 11.9s
Precision: 64
Internal Precision: 320
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\sqrt{{\left(e^{-1}\right)}^{\left(1 - x \cdot x\right)}} \cdot \sqrt{{\left(e^{-1}\right)}^{\left(1 - x \cdot x\right)}}\]

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. Using strategy rm

  3. Applied neg-mul-10.0

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

  4. Applied exp-prod0.0

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

  6. Applied add-sqr-sqrt0.0

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

  7. Final simplification0.0

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

Runtime

Time bar (total: 11.9s)Debug logProfile

herbie shell --seed 2018215 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))