Average Error: 0.1 → 0.2
Time: 1.5m
Precision: 64
Internal Precision: 576
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot \sqrt{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}} \cdot rand\right)\]

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 add-sqr-sqrt0.2

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

Runtime

Time bar (total: 1.5m)Debug logProfile

herbie shell --seed 2018206 
(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))))