Average Error: 0.1 → 0.1
Time: 19.6s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(\frac{rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} + 1\right) \cdot \left(1 \cdot \left(a - \frac{1}{3}\right)\right)\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\left(\frac{rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} + 1\right) \cdot \left(1 \cdot \left(a - \frac{1}{3}\right)\right)
double f(double a, double rand) {
        double r56846 = a;
        double r56847 = 1.0;
        double r56848 = 3.0;
        double r56849 = r56847 / r56848;
        double r56850 = r56846 - r56849;
        double r56851 = 9.0;
        double r56852 = r56851 * r56850;
        double r56853 = sqrt(r56852);
        double r56854 = r56847 / r56853;
        double r56855 = rand;
        double r56856 = r56854 * r56855;
        double r56857 = r56847 + r56856;
        double r56858 = r56850 * r56857;
        return r56858;
}
↓
double f(double a, double rand) {
        double r56859 = rand;
        double r56860 = 9.0;
        double r56861 = a;
        double r56862 = 1.0;
        double r56863 = 3.0;
        double r56864 = r56862 / r56863;
        double r56865 = r56861 - r56864;
        double r56866 = r56860 * r56865;
        double r56867 = sqrt(r56866);
        double r56868 = r56859 / r56867;
        double r56869 = 1.0;
        double r56870 = r56868 + r56869;
        double r56871 = r56862 * r56865;
        double r56872 = r56870 * r56871;
        return r56872;
}

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-sqr-sqrt0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019298 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))