Average Error: 0.1 → 0.1
Time: 25.6s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\frac{rand}{\sqrt{\left(a - \frac{1.0}{3.0}\right) \cdot 9}} \cdot \left(a - \frac{1.0}{3.0}\right) + \left(a - \frac{1.0}{3.0}\right)\]
\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)
↓
\frac{rand}{\sqrt{\left(a - \frac{1.0}{3.0}\right) \cdot 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 r3896826 = a;
        double r3896827 = 1.0;
        double r3896828 = 3.0;
        double r3896829 = r3896827 / r3896828;
        double r3896830 = r3896826 - r3896829;
        double r3896831 = 1.0;
        double r3896832 = 9.0;
        double r3896833 = r3896832 * r3896830;
        double r3896834 = sqrt(r3896833);
        double r3896835 = r3896831 / r3896834;
        double r3896836 = rand;
        double r3896837 = r3896835 * r3896836;
        double r3896838 = r3896831 + r3896837;
        double r3896839 = r3896830 * r3896838;
        return r3896839;
}
↓
double f(double a, double rand) {
        double r3896840 = rand;
        double r3896841 = a;
        double r3896842 = 1.0;
        double r3896843 = 3.0;
        double r3896844 = r3896842 / r3896843;
        double r3896845 = r3896841 - r3896844;
        double r3896846 = 9.0;
        double r3896847 = r3896845 * r3896846;
        double r3896848 = sqrt(r3896847);
        double r3896849 = r3896840 / r3896848;
        double r3896850 = r3896849 * r3896845;
        double r3896851 = r3896850 + r3896845;
        return r3896851;
}

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. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019132 
(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))))