Average Error: 0.1 → 0.1
Time: 1.6m
Precision: 64
Internal Precision: 576
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(1 + \frac{rand}{\sqrt{\left(a - \frac{1.0}{3.0}\right) \cdot 9}}\right) \cdot \left(a - \frac{1.0}{3.0}\right)\]

Error

Bits error versus a

Bits error versus rand

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  3. Applied *-un-lft-identity0.1

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

  4. Applied associate-*r*0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed 2018254 
(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))))