Average Error: 0.1 → 0.1
Time: 1.2m
Precision: 64
Internal Precision: 128
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\frac{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}{rand}}\right)\]

Error

Bits error versus a

Bits error versus rand

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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 associate-*l/0.1

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

  4. Simplified0.1

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

  6. Applied clear-num0.1

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

  7. Final simplification0.1

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

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018348 
(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))))