Error

Derivation

1. Initial program 0.1

   \[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]

2. Initial simplification0.1

   \[\leadsto (\left(\frac{a - \frac{1.0}{3.0}}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}\right) \cdot rand + \left(a - \frac{1.0}{3.0}\right))_*\]
3. Using strategy rm

4. Applied sqrt-prod0.1

   \[\leadsto (\left(\frac{a - \frac{1.0}{3.0}}{\color{blue}{\sqrt{9} \cdot \sqrt{a - \frac{1.0}{3.0}}}}\right) \cdot rand + \left(a - \frac{1.0}{3.0}\right))_*\]

5. Applied add-sqr-sqrt0.2

   \[\leadsto (\left(\frac{\color{blue}{\sqrt{a - \frac{1.0}{3.0}} \cdot \sqrt{a - \frac{1.0}{3.0}}}}{\sqrt{9} \cdot \sqrt{a - \frac{1.0}{3.0}}}\right) \cdot rand + \left(a - \frac{1.0}{3.0}\right))_*\]

6. Applied times-frac0.1

   \[\leadsto (\color{blue}{\left(\frac{\sqrt{a - \frac{1.0}{3.0}}}{\sqrt{9}} \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{\sqrt{a - \frac{1.0}{3.0}}}\right)} \cdot rand + \left(a - \frac{1.0}{3.0}\right))_*\]

7. Simplified0.1

   \[\leadsto (\left(\color{blue}{\frac{\sqrt{a - \frac{1.0}{3.0}}}{3}} \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{\sqrt{a - \frac{1.0}{3.0}}}\right) \cdot rand + \left(a - \frac{1.0}{3.0}\right))_*\]

8. Simplified0.1

   \[\leadsto (\left(\frac{\sqrt{a - \frac{1.0}{3.0}}}{3} \cdot \color{blue}{1}\right) \cdot rand + \left(a - \frac{1.0}{3.0}\right))_*\]

9. Final simplification0.1

   \[\leadsto (\left(\frac{\sqrt{a - \frac{1.0}{3.0}}}{3}\right) \cdot rand + \left(a - \frac{1.0}{3.0}\right))_*\]

Runtime

Time bar (total: 31.2s)Debug logProfile

herbie shell --seed 2018339 +o rules:numerics
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))))