Average Error: 26.3 → 26.2
Time: 1.0m
Precision: 64
Internal Precision: 128
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\log \left(e^{\frac{\left(a - \frac{1.0}{3.0}\right) \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}}\right) + \left(a - \frac{1.0}{3.0}\right)\]

Error

Bits error versus a

Bits error versus rand

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Your Program's Arguments

Results

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Derivation

  1. Initial program 26.3

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

  2. Initial simplification26.3

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

  4. Applied add-log-exp26.2

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

  5. Final simplification26.2

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

Runtime

Time bar (total: 1.0m)Debug logProfile

herbie shell --seed 2018255 
(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))))