Average Error: 0.1 → 0.1
Time: 25.1s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(1 + \frac{rand \cdot 1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot \left(a - \frac{1}{3}\right)\]
\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 + \frac{rand \cdot 1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot \left(a - \frac{1}{3}\right)
double f(double a, double rand) {
        double r3413854 = a;
        double r3413855 = 1.0;
        double r3413856 = 3.0;
        double r3413857 = r3413855 / r3413856;
        double r3413858 = r3413854 - r3413857;
        double r3413859 = 9.0;
        double r3413860 = r3413859 * r3413858;
        double r3413861 = sqrt(r3413860);
        double r3413862 = r3413855 / r3413861;
        double r3413863 = rand;
        double r3413864 = r3413862 * r3413863;
        double r3413865 = r3413855 + r3413864;
        double r3413866 = r3413858 * r3413865;
        return r3413866;
}
↓
double f(double a, double rand) {
        double r3413867 = 1.0;
        double r3413868 = rand;
        double r3413869 = r3413868 * r3413867;
        double r3413870 = 9.0;
        double r3413871 = a;
        double r3413872 = 3.0;
        double r3413873 = r3413867 / r3413872;
        double r3413874 = r3413871 - r3413873;
        double r3413875 = r3413870 * r3413874;
        double r3413876 = sqrt(r3413875);
        double r3413877 = r3413869 / r3413876;
        double r3413878 = r3413867 + r3413877;
        double r3413879 = r3413878 * r3413874;
        return r3413879;
}

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

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

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))))