Average Error: 0.1 → 0.1
Time: 22.5s
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 r83828 = a;
        double r83829 = 1.0;
        double r83830 = 3.0;
        double r83831 = r83829 / r83830;
        double r83832 = r83828 - r83831;
        double r83833 = 9.0;
        double r83834 = r83833 * r83832;
        double r83835 = sqrt(r83834);
        double r83836 = r83829 / r83835;
        double r83837 = rand;
        double r83838 = r83836 * r83837;
        double r83839 = r83829 + r83838;
        double r83840 = r83832 * r83839;
        return r83840;
}
↓
double f(double a, double rand) {
        double r83841 = a;
        double r83842 = 1.0;
        double r83843 = 3.0;
        double r83844 = r83842 / r83843;
        double r83845 = r83841 - r83844;
        double r83846 = rand;
        double r83847 = r83842 * r83846;
        double r83848 = 9.0;
        double r83849 = r83848 * r83845;
        double r83850 = sqrt(r83849);
        double r83851 = r83847 / r83850;
        double r83852 = r83842 + r83851;
        double r83853 = r83845 * r83852;
        return r83853;
}

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 distribute-lft-in0.1

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

  6. 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 2019303 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))