Average Error: 0.1 → 0.2
Time: 1.3m
Precision: 64
Internal Precision: 128
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(1 + \frac{1}{3 \cdot \sqrt{a - \frac{1.0}{3.0}}} \cdot rand\right) \cdot \left(a - \frac{1.0}{3.0}\right)\]

Error

Bits error versus a

Bits error versus rand

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Your Program's Arguments

Results

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 sqrt-prod0.2

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

  4. Simplified0.2

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\color{blue}{3} \cdot \sqrt{a - \frac{1.0}{3.0}}} \cdot rand\right)\]
  5. Using strategy rm

  6. Applied *-commutative0.2

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

  7. Final simplification0.2

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

Runtime

Time bar (total: 1.3m)Debug logProfile

herbie shell --seed 2018273 
(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))))