Average Error: 0.1 → 0.1
Time: 24.1s
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 r1400810 = a;
        double r1400811 = 1.0;
        double r1400812 = 3.0;
        double r1400813 = r1400811 / r1400812;
        double r1400814 = r1400810 - r1400813;
        double r1400815 = 1.0;
        double r1400816 = 9.0;
        double r1400817 = r1400816 * r1400814;
        double r1400818 = sqrt(r1400817);
        double r1400819 = r1400815 / r1400818;
        double r1400820 = rand;
        double r1400821 = r1400819 * r1400820;
        double r1400822 = r1400815 + r1400821;
        double r1400823 = r1400814 * r1400822;
        return r1400823;
}
↓
double f(double a, double rand) {
        double r1400824 = a;
        double r1400825 = 1.0;
        double r1400826 = 3.0;
        double r1400827 = r1400825 / r1400826;
        double r1400828 = r1400824 - r1400827;
        double r1400829 = rand;
        double r1400830 = 9.0;
        double r1400831 = r1400830 * r1400828;
        double r1400832 = sqrt(r1400831);
        double r1400833 = r1400829 / r1400832;
        double r1400834 = r1400828 * r1400833;
        double r1400835 = r1400834 + r1400828;
        return r1400835;
}

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

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

  3. 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 2019152 
(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))))