Average Error: 0.1 → 0.1
Time: 26.3s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(1 + 1 \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot \left(a - \frac{1}{3}\right)\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\left(1 + 1 \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot \left(a - \frac{1}{3}\right)
double f(double a, double rand) {
        double r3132892 = a;
        double r3132893 = 1.0;
        double r3132894 = 3.0;
        double r3132895 = r3132893 / r3132894;
        double r3132896 = r3132892 - r3132895;
        double r3132897 = 9.0;
        double r3132898 = r3132897 * r3132896;
        double r3132899 = sqrt(r3132898);
        double r3132900 = r3132893 / r3132899;
        double r3132901 = rand;
        double r3132902 = r3132900 * r3132901;
        double r3132903 = r3132893 + r3132902;
        double r3132904 = r3132896 * r3132903;
        return r3132904;
}
↓
double f(double a, double rand) {
        double r3132905 = 1.0;
        double r3132906 = rand;
        double r3132907 = 9.0;
        double r3132908 = a;
        double r3132909 = 3.0;
        double r3132910 = r3132905 / r3132909;
        double r3132911 = r3132908 - r3132910;
        double r3132912 = r3132907 * r3132911;
        double r3132913 = sqrt(r3132912);
        double r3132914 = r3132906 / r3132913;
        double r3132915 = r3132905 * r3132914;
        double r3132916 = r3132905 + r3132915;
        double r3132917 = r3132916 * r3132911;
        return r3132917;
}

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 div-inv0.1

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

  4. Applied associate-*l*0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))))