Average Error: 0.1 → 0.1
Time: 21.4s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(\frac{rand \cdot 1}{\sqrt{\sqrt{9} \cdot \left(\left(a - \frac{1}{3}\right) \cdot \sqrt{9}\right)}} + 1\right) \cdot \left(a - \frac{1}{3}\right)\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\left(\frac{rand \cdot 1}{\sqrt{\sqrt{9} \cdot \left(\left(a - \frac{1}{3}\right) \cdot \sqrt{9}\right)}} + 1\right) \cdot \left(a - \frac{1}{3}\right)
double f(double a, double rand) {
        double r128835 = a;
        double r128836 = 1.0;
        double r128837 = 3.0;
        double r128838 = r128836 / r128837;
        double r128839 = r128835 - r128838;
        double r128840 = 9.0;
        double r128841 = r128840 * r128839;
        double r128842 = sqrt(r128841);
        double r128843 = r128836 / r128842;
        double r128844 = rand;
        double r128845 = r128843 * r128844;
        double r128846 = r128836 + r128845;
        double r128847 = r128839 * r128846;
        return r128847;
}
↓
double f(double a, double rand) {
        double r128848 = rand;
        double r128849 = 1.0;
        double r128850 = r128848 * r128849;
        double r128851 = 9.0;
        double r128852 = sqrt(r128851);
        double r128853 = a;
        double r128854 = 3.0;
        double r128855 = r128849 / r128854;
        double r128856 = r128853 - r128855;
        double r128857 = r128856 * r128852;
        double r128858 = r128852 * r128857;
        double r128859 = sqrt(r128858);
        double r128860 = r128850 / r128859;
        double r128861 = r128860 + r128849;
        double r128862 = r128861 * r128856;
        return r128862;
}

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

    \[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
  2. Using strategy rm

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

    \[\leadsto \color{blue}{\left(1 \cdot \left(a - \frac{1}{3}\right)\right)} \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]

  4. Applied associate-*l*0.1

    \[\leadsto \color{blue}{1 \cdot \left(\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\right)}\]

  5. Simplified0.1

    \[\leadsto 1 \cdot \color{blue}{\left(\left(1 + \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot \left(a - \frac{1}{3}\right)\right)}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt0.1

    \[\leadsto 1 \cdot \left(\left(1 + \frac{1 \cdot rand}{\sqrt{\color{blue}{\left(\sqrt{9} \cdot \sqrt{9}\right)} \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot \left(a - \frac{1}{3}\right)\right)\]

  8. Applied associate-*l*0.1

    \[\leadsto 1 \cdot \left(\left(1 + \frac{1 \cdot rand}{\sqrt{\color{blue}{\sqrt{9} \cdot \left(\sqrt{9} \cdot \left(a - \frac{1}{3}\right)\right)}}}\right) \cdot \left(a - \frac{1}{3}\right)\right)\]

  9. Final simplification0.1

    \[\leadsto \left(\frac{rand \cdot 1}{\sqrt{\sqrt{9} \cdot \left(\left(a - \frac{1}{3}\right) \cdot \sqrt{9}\right)}} + 1\right) \cdot \left(a - \frac{1}{3}\right)\]

Reproduce

herbie shell --seed 2019174 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))))