Average Error: 0.1 → 0.1
Time: 1.4m
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[a - \left(\frac{1.0}{3.0} - \left(a - \frac{1.0}{3.0}\right) \cdot \frac{\frac{rand}{3}}{\sqrt{a - \frac{1.0}{3.0}}}\right)\]
\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)
↓
a - \left(\frac{1.0}{3.0} - \left(a - \frac{1.0}{3.0}\right) \cdot \frac{\frac{rand}{3}}{\sqrt{a - \frac{1.0}{3.0}}}\right)
double f(double a, double rand) {
        double r3743418 = a;
        double r3743419 = 1.0;
        double r3743420 = 3.0;
        double r3743421 = r3743419 / r3743420;
        double r3743422 = r3743418 - r3743421;
        double r3743423 = 1.0;
        double r3743424 = 9.0;
        double r3743425 = r3743424 * r3743422;
        double r3743426 = sqrt(r3743425);
        double r3743427 = r3743423 / r3743426;
        double r3743428 = rand;
        double r3743429 = r3743427 * r3743428;
        double r3743430 = r3743423 + r3743429;
        double r3743431 = r3743422 * r3743430;
        return r3743431;
}
↓
double f(double a, double rand) {
        double r3743432 = a;
        double r3743433 = 1.0;
        double r3743434 = 3.0;
        double r3743435 = r3743433 / r3743434;
        double r3743436 = r3743432 - r3743435;
        double r3743437 = rand;
        double r3743438 = 3.0;
        double r3743439 = r3743437 / r3743438;
        double r3743440 = sqrt(r3743436);
        double r3743441 = r3743439 / r3743440;
        double r3743442 = r3743436 * r3743441;
        double r3743443 = r3743435 - r3743442;
        double r3743444 = r3743432 - r3743443;
        return r3743444;
}

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

    \[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\left(a - \frac{1.0}{3.0}\right) + \left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}}\]
  3. Using strategy rm

  4. Applied sqrt-prod0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand}{\color{blue}{\sqrt{9} \cdot \sqrt{a - \frac{1.0}{3.0}}}}\]

  5. Applied associate-/r*0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \left(a - \frac{1.0}{3.0}\right) \cdot \color{blue}{\frac{\frac{rand}{\sqrt{9}}}{\sqrt{a - \frac{1.0}{3.0}}}}\]

  6. Simplified0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \left(a - \frac{1.0}{3.0}\right) \cdot \frac{\color{blue}{\frac{rand}{3}}}{\sqrt{a - \frac{1.0}{3.0}}}\]
  7. Using strategy rm

  8. Applied associate-+l-0.1

    \[\leadsto \color{blue}{a - \left(\frac{1.0}{3.0} - \left(a - \frac{1.0}{3.0}\right) \cdot \frac{\frac{rand}{3}}{\sqrt{a - \frac{1.0}{3.0}}}\right)}\]

  9. Final simplification0.1

    \[\leadsto a - \left(\frac{1.0}{3.0} - \left(a - \frac{1.0}{3.0}\right) \cdot \frac{\frac{rand}{3}}{\sqrt{a - \frac{1.0}{3.0}}}\right)\]

Reproduce

herbie shell --seed 2019154 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))))