Average Error: 0.0 → 0.0
Time: 4.7s
Precision: 64
Internal Precision: 128
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{\sqrt[3]{{\left(e^{x}\right)}^{x}} \cdot \left(\sqrt[3]{{\left(e^{x}\right)}^{x}} \cdot \sqrt[3]{\sqrt[3]{{\left(e^{x}\right)}^{x}} \cdot \left(\sqrt[3]{{\left(e^{x}\right)}^{x}} \cdot \sqrt[3]{{\left(e^{x}\right)}^{x}}\right)}\right)}{e}\]

Error

Bits error versus x

Try it out

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. Simplified0.0

    \[\leadsto \color{blue}{\frac{e^{x \cdot x}}{e}}\]
  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-cube-cbrt0.0

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{{\left(e^{x}\right)}^{x}} \cdot \sqrt[3]{{\left(e^{x}\right)}^{x}}\right) \cdot \sqrt[3]{{\left(e^{x}\right)}^{x}}}}{e}\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019026 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))