Average Error: 0.1 → 0.1
Time: 6.6s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\]
\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 r81324 = a;
        double r81325 = 1.0;
        double r81326 = 3.0;
        double r81327 = r81325 / r81326;
        double r81328 = r81324 - r81327;
        double r81329 = 9.0;
        double r81330 = r81329 * r81328;
        double r81331 = sqrt(r81330);
        double r81332 = r81325 / r81331;
        double r81333 = rand;
        double r81334 = r81332 * r81333;
        double r81335 = r81325 + r81334;
        double r81336 = r81328 * r81335;
        return r81336;
}
↓
double f(double a, double rand) {
        double r81337 = a;
        double r81338 = 1.0;
        double r81339 = 3.0;
        double r81340 = r81338 / r81339;
        double r81341 = r81337 - r81340;
        double r81342 = r81341 * r81338;
        double r81343 = rand;
        double r81344 = r81338 * r81343;
        double r81345 = 9.0;
        double r81346 = r81345 * r81341;
        double r81347 = sqrt(r81346);
        double r81348 = r81344 / r81347;
        double r81349 = r81341 * r81348;
        double r81350 = r81342 + r81349;
        return r81350;
}

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 distribute-lft-in0.1

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

  5. Applied associate-*l/0.1

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

  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 2020056 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))