Average Error: 0.1 → 0.1
Time: 26.2s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(\frac{1}{\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}} \cdot rand\right) + 1 \cdot \left(a - \frac{1}{3}\right)\]
\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 \left(\frac{1}{\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}} \cdot rand\right) + 1 \cdot \left(a - \frac{1}{3}\right)
double f(double a, double rand) {
        double r3255468 = a;
        double r3255469 = 1.0;
        double r3255470 = 3.0;
        double r3255471 = r3255469 / r3255470;
        double r3255472 = r3255468 - r3255471;
        double r3255473 = 9.0;
        double r3255474 = r3255473 * r3255472;
        double r3255475 = sqrt(r3255474);
        double r3255476 = r3255469 / r3255475;
        double r3255477 = rand;
        double r3255478 = r3255476 * r3255477;
        double r3255479 = r3255469 + r3255478;
        double r3255480 = r3255472 * r3255479;
        return r3255480;
}
↓
double f(double a, double rand) {
        double r3255481 = a;
        double r3255482 = 1.0;
        double r3255483 = 3.0;
        double r3255484 = r3255482 / r3255483;
        double r3255485 = r3255481 - r3255484;
        double r3255486 = 9.0;
        double r3255487 = sqrt(r3255486);
        double r3255488 = sqrt(r3255485);
        double r3255489 = r3255487 * r3255488;
        double r3255490 = r3255482 / r3255489;
        double r3255491 = rand;
        double r3255492 = r3255490 * r3255491;
        double r3255493 = r3255485 * r3255492;
        double r3255494 = r3255482 * r3255485;
        double r3255495 = r3255493 + r3255494;
        return r3255495;
}

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 sqrt-prod0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))))