Average Error: 0.2 → 0.0
Time: 25.5s
Precision: 64
Internal Precision: 576
\[\frac{1}{\sqrt{\left({e}^{\left({x}^{2}\right)} \cdot 2\right) \cdot pi}}\]
\[{\left(\left(2 \cdot pi\right) \cdot \left(\sqrt[3]{{e}^{\left(x \cdot x\right)}} \cdot \left(\sqrt[3]{{e}^{\left(x \cdot x\right)}} \cdot \sqrt[3]{{e}^{\left(x \cdot x\right)}}\right)\right)\right)}^{\left(-\frac{1}{2}\right)}\]

Error

Bits error versus e

Bits error versus x

Bits error versus pi

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{1}{\sqrt{\left({e}^{\left({x}^{2}\right)} \cdot 2\right) \cdot pi}}\]
  2. Initial simplification0.2

    \[\leadsto \frac{1}{\sqrt{{e}^{\left(x \cdot x\right)} \cdot \left(pi \cdot 2\right)}}\]
  3. Using strategy rm
  4. Applied pow1/20.1

    \[\leadsto \frac{1}{\color{blue}{{\left({e}^{\left(x \cdot x\right)} \cdot \left(pi \cdot 2\right)\right)}^{\frac{1}{2}}}}\]
  5. Applied pow-flip0.0

    \[\leadsto \color{blue}{{\left({e}^{\left(x \cdot x\right)} \cdot \left(pi \cdot 2\right)\right)}^{\left(-\frac{1}{2}\right)}}\]
  6. Using strategy rm
  7. Applied add-cube-cbrt0.0

    \[\leadsto {\left(\color{blue}{\left(\left(\sqrt[3]{{e}^{\left(x \cdot x\right)}} \cdot \sqrt[3]{{e}^{\left(x \cdot x\right)}}\right) \cdot \sqrt[3]{{e}^{\left(x \cdot x\right)}}\right)} \cdot \left(pi \cdot 2\right)\right)}^{\left(-\frac{1}{2}\right)}\]
  8. Final simplification0.0

    \[\leadsto {\left(\left(2 \cdot pi\right) \cdot \left(\sqrt[3]{{e}^{\left(x \cdot x\right)}} \cdot \left(\sqrt[3]{{e}^{\left(x \cdot x\right)}} \cdot \sqrt[3]{{e}^{\left(x \cdot x\right)}}\right)\right)\right)}^{\left(-\frac{1}{2}\right)}\]

Runtime

Time bar (total: 25.5s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (e x pi)
  :name "1 / sqrt(e^(x^2) * 2 * pi)"
  (/ 1 (sqrt (* (* (pow e (pow x 2)) 2) pi))))