Average Error: 0.1 → 0.1
Time: 7.9s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\left(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)}}
double f(double a, double rand) {
        double r106328 = a;
        double r106329 = 1.0;
        double r106330 = 3.0;
        double r106331 = r106329 / r106330;
        double r106332 = r106328 - r106331;
        double r106333 = 9.0;
        double r106334 = r106333 * r106332;
        double r106335 = sqrt(r106334);
        double r106336 = r106329 / r106335;
        double r106337 = rand;
        double r106338 = r106336 * r106337;
        double r106339 = r106329 + r106338;
        double r106340 = r106332 * r106339;
        return r106340;
}
↓
double f(double a, double rand) {
        double r106341 = a;
        double r106342 = 1.0;
        double r106343 = 3.0;
        double r106344 = r106342 / r106343;
        double r106345 = r106341 - r106344;
        double r106346 = r106345 * r106342;
        double r106347 = rand;
        double r106348 = r106342 * r106347;
        double r106349 = 9.0;
        double r106350 = r106349 * r106345;
        double r106351 = sqrt(r106350);
        double r106352 = r106348 / r106351;
        double r106353 = r106345 * r106352;
        double r106354 = r106346 + r106353;
        return r106354;
}

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

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

Reproduce

herbie shell --seed 2020034 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))