Average Error: 0.0 → 0.0
Time: 9.5s
Precision: 64
Internal Precision: 320
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\sqrt[3]{\frac{{\left(e^{x}\right)}^{x}}{e} \cdot \left(\frac{{\left(e^{x}\right)}^{x}}{e} \cdot \frac{{\left(e^{x}\right)}^{x}}{e}\right)}\]

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

    \[\leadsto \frac{e^{x \cdot x}}{e}\]
  3. Using strategy rm

  4. Applied exp-prod0.0

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

  6. Applied add-cbrt-cube0.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{{\left(e^{x}\right)}^{x}}{e} \cdot \frac{{\left(e^{x}\right)}^{x}}{e}\right) \cdot \frac{{\left(e^{x}\right)}^{x}}{e}}}\]

  7. Final simplification0.0

    \[\leadsto \sqrt[3]{\frac{{\left(e^{x}\right)}^{x}}{e} \cdot \left(\frac{{\left(e^{x}\right)}^{x}}{e} \cdot \frac{{\left(e^{x}\right)}^{x}}{e}\right)}\]

Runtime

Time bar (total: 9.5s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.00.00.00.00%
herbie shell --seed 2018339 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))