Average Error: 0.1 → 0.1
Time: 26.8s
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 r3255511 = a;
        double r3255512 = 1.0;
        double r3255513 = 3.0;
        double r3255514 = r3255512 / r3255513;
        double r3255515 = r3255511 - r3255514;
        double r3255516 = 9.0;
        double r3255517 = r3255516 * r3255515;
        double r3255518 = sqrt(r3255517);
        double r3255519 = r3255512 / r3255518;
        double r3255520 = rand;
        double r3255521 = r3255519 * r3255520;
        double r3255522 = r3255512 + r3255521;
        double r3255523 = r3255515 * r3255522;
        return r3255523;
}
↓
double f(double a, double rand) {
        double r3255524 = a;
        double r3255525 = 1.0;
        double r3255526 = 3.0;
        double r3255527 = r3255525 / r3255526;
        double r3255528 = r3255524 - r3255527;
        double r3255529 = 9.0;
        double r3255530 = sqrt(r3255529);
        double r3255531 = sqrt(r3255528);
        double r3255532 = r3255530 * r3255531;
        double r3255533 = r3255525 / r3255532;
        double r3255534 = rand;
        double r3255535 = r3255533 * r3255534;
        double r3255536 = r3255528 * r3255535;
        double r3255537 = r3255525 * r3255528;
        double r3255538 = r3255536 + r3255537;
        return r3255538;
}

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))))