Average Error: 7.9 → 0.0
Time: 20.5s
Precision: 64
Internal Precision: 576
\[e^{\frac{\left(-\left(x - a\right)\right) \cdot \left(x - a\right)}{\left(2 \cdot b\right) \cdot b}}\]
\[e^{\frac{x - a}{2} \cdot \frac{\frac{a - x}{b}}{b}}\]

Error

Bits error versus x

Bits error versus a

Bits error versus b

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Results

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Derivation

  1. Initial program 7.9

    \[e^{\frac{\left(-\left(x - a\right)\right) \cdot \left(x - a\right)}{\left(2 \cdot b\right) \cdot b}}\]
  2. Initial simplification4.0

    \[\leadsto e^{\frac{x - a}{2} \cdot \frac{a - x}{b \cdot b}}\]
  3. Using strategy rm
  4. Applied associate-/r*0.0

    \[\leadsto e^{\frac{x - a}{2} \cdot \color{blue}{\frac{\frac{a - x}{b}}{b}}}\]
  5. Final simplification0.0

    \[\leadsto e^{\frac{x - a}{2} \cdot \frac{\frac{a - x}{b}}{b}}\]

Runtime

Time bar (total: 20.5s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x a b)
  :name "exp(-(x-a)*(x-a)/(2*b*b))"
  (exp (/ (* (- (- x a)) (- x a)) (* (* 2 b) b))))