Error

Try it out

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-sqr-sqrt0.0

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

7. Applied associate-/l*0.0

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

9. Applied div-inv0.0

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

10. Applied add-cube-cbrt0.0

    \[\leadsto \frac{\sqrt{\color{blue}{\left(\sqrt[3]{{\left(e^{x}\right)}^{x}} \cdot \sqrt[3]{{\left(e^{x}\right)}^{x}}\right) \cdot \sqrt[3]{{\left(e^{x}\right)}^{x}}}}}{e \cdot \frac{1}{\sqrt{{\left(e^{x}\right)}^{x}}}}\]

11. Applied sqrt-prod0.0

    \[\leadsto \frac{\color{blue}{\sqrt{\sqrt[3]{{\left(e^{x}\right)}^{x}} \cdot \sqrt[3]{{\left(e^{x}\right)}^{x}}} \cdot \sqrt{\sqrt[3]{{\left(e^{x}\right)}^{x}}}}}{e \cdot \frac{1}{\sqrt{{\left(e^{x}\right)}^{x}}}}\]

12. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{\sqrt{\sqrt[3]{{\left(e^{x}\right)}^{x}} \cdot \sqrt[3]{{\left(e^{x}\right)}^{x}}}}{e} \cdot \frac{\sqrt{\sqrt[3]{{\left(e^{x}\right)}^{x}}}}{\frac{1}{\sqrt{{\left(e^{x}\right)}^{x}}}}}\]

13. Simplified0.0

    \[\leadsto \color{blue}{\frac{\left|\sqrt[3]{{\left(e^{x}\right)}^{x}}\right|}{e}} \cdot \frac{\sqrt{\sqrt[3]{{\left(e^{x}\right)}^{x}}}}{\frac{1}{\sqrt{{\left(e^{x}\right)}^{x}}}}\]

14. Simplified0.0

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

15. Final simplification0.0

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

Reproduce

herbie shell --seed 2018365 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))

Details

Time bar (total: 7.4s)Debug log