Average Error: 0.1 → 0.1
Time: 6.7s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{\left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(\sqrt[3]{9} \cdot \left(a - \frac{1}{3}\right)\right)}}\right)\]
\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{\left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(\sqrt[3]{9} \cdot \left(a - \frac{1}{3}\right)\right)}}\right)
double f(double a, double rand) {
        double r91870 = a;
        double r91871 = 1.0;
        double r91872 = 3.0;
        double r91873 = r91871 / r91872;
        double r91874 = r91870 - r91873;
        double r91875 = 9.0;
        double r91876 = r91875 * r91874;
        double r91877 = sqrt(r91876);
        double r91878 = r91871 / r91877;
        double r91879 = rand;
        double r91880 = r91878 * r91879;
        double r91881 = r91871 + r91880;
        double r91882 = r91874 * r91881;
        return r91882;
}
↓
double f(double a, double rand) {
        double r91883 = a;
        double r91884 = 1.0;
        double r91885 = 3.0;
        double r91886 = r91884 / r91885;
        double r91887 = r91883 - r91886;
        double r91888 = rand;
        double r91889 = r91884 * r91888;
        double r91890 = 9.0;
        double r91891 = cbrt(r91890);
        double r91892 = r91891 * r91891;
        double r91893 = r91891 * r91887;
        double r91894 = r91892 * r91893;
        double r91895 = sqrt(r91894);
        double r91896 = r91889 / r91895;
        double r91897 = r91884 + r91896;
        double r91898 = r91887 * r91897;
        return r91898;
}

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. Using strategy rm

  5. Applied add-cube-cbrt0.1

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

  6. Applied associate-*l*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020001 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))