Average Error: 0.1 → 0.1
Time: 21.2s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} + \left(a - \frac{1.0}{3.0}\right)\]
\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 \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} + \left(a - \frac{1.0}{3.0}\right)
double f(double a, double rand) {
        double r4256821 = a;
        double r4256822 = 1.0;
        double r4256823 = 3.0;
        double r4256824 = r4256822 / r4256823;
        double r4256825 = r4256821 - r4256824;
        double r4256826 = 1.0;
        double r4256827 = 9.0;
        double r4256828 = r4256827 * r4256825;
        double r4256829 = sqrt(r4256828);
        double r4256830 = r4256826 / r4256829;
        double r4256831 = rand;
        double r4256832 = r4256830 * r4256831;
        double r4256833 = r4256826 + r4256832;
        double r4256834 = r4256825 * r4256833;
        return r4256834;
}
↓
double f(double a, double rand) {
        double r4256835 = a;
        double r4256836 = 1.0;
        double r4256837 = 3.0;
        double r4256838 = r4256836 / r4256837;
        double r4256839 = r4256835 - r4256838;
        double r4256840 = rand;
        double r4256841 = 9.0;
        double r4256842 = r4256841 * r4256839;
        double r4256843 = sqrt(r4256842);
        double r4256844 = r4256840 / r4256843;
        double r4256845 = r4256839 * r4256844;
        double r4256846 = r4256845 + r4256839;
        return r4256846;
}

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 distribute-lft-in0.1

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

  4. Simplified0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019164 
(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))))