Average Error: 0.1 → 0.1
Time: 8.1s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right)\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right)
double f(double a, double rand) {
        double r73875 = a;
        double r73876 = 1.0;
        double r73877 = 3.0;
        double r73878 = r73876 / r73877;
        double r73879 = r73875 - r73878;
        double r73880 = 9.0;
        double r73881 = r73880 * r73879;
        double r73882 = sqrt(r73881);
        double r73883 = r73876 / r73882;
        double r73884 = rand;
        double r73885 = r73883 * r73884;
        double r73886 = r73876 + r73885;
        double r73887 = r73879 * r73886;
        return r73887;
}
↓
double f(double a, double rand) {
        double r73888 = a;
        double r73889 = 1.0;
        double r73890 = 3.0;
        double r73891 = r73889 / r73890;
        double r73892 = r73888 - r73891;
        double r73893 = rand;
        double r73894 = r73889 * r73893;
        double r73895 = 9.0;
        double r73896 = r73895 * r73892;
        double r73897 = sqrt(r73896);
        double r73898 = r73894 / r73897;
        double r73899 = r73889 + r73898;
        double r73900 = r73892 * r73899;
        return r73900;
}

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 associate-*l/0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020003 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))