Average Error: 0.1 → 0.1
Time: 30.7s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[rand \cdot \left(\frac{a}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} - \frac{\frac{1.0}{3.0}}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}\right) + \left(a - \frac{1.0}{3.0}\right)\]
\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)
↓
rand \cdot \left(\frac{a}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} - \frac{\frac{1.0}{3.0}}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}\right) + \left(a - \frac{1.0}{3.0}\right)
double f(double a, double rand) {
        double r2552673 = a;
        double r2552674 = 1.0;
        double r2552675 = 3.0;
        double r2552676 = r2552674 / r2552675;
        double r2552677 = r2552673 - r2552676;
        double r2552678 = 1.0;
        double r2552679 = 9.0;
        double r2552680 = r2552679 * r2552677;
        double r2552681 = sqrt(r2552680);
        double r2552682 = r2552678 / r2552681;
        double r2552683 = rand;
        double r2552684 = r2552682 * r2552683;
        double r2552685 = r2552678 + r2552684;
        double r2552686 = r2552677 * r2552685;
        return r2552686;
}
↓
double f(double a, double rand) {
        double r2552687 = rand;
        double r2552688 = a;
        double r2552689 = 9.0;
        double r2552690 = 1.0;
        double r2552691 = 3.0;
        double r2552692 = r2552690 / r2552691;
        double r2552693 = r2552688 - r2552692;
        double r2552694 = r2552689 * r2552693;
        double r2552695 = sqrt(r2552694);
        double r2552696 = r2552688 / r2552695;
        double r2552697 = r2552692 / r2552695;
        double r2552698 = r2552696 - r2552697;
        double r2552699 = r2552687 * r2552698;
        double r2552700 = r2552699 + r2552693;
        return r2552700;
}

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

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

  4. Applied div-sub0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019146 
(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))))