Average Error: 0.1 → 0.1
Time: 28.9s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
\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(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
double f(double a, double rand) {
        double r131595 = a;
        double r131596 = 1.0;
        double r131597 = 3.0;
        double r131598 = r131596 / r131597;
        double r131599 = r131595 - r131598;
        double r131600 = 9.0;
        double r131601 = r131600 * r131599;
        double r131602 = sqrt(r131601);
        double r131603 = r131596 / r131602;
        double r131604 = rand;
        double r131605 = r131603 * r131604;
        double r131606 = r131596 + r131605;
        double r131607 = r131599 * r131606;
        return r131607;
}
↓
double f(double a, double rand) {
        double r131608 = a;
        double r131609 = 1.0;
        double r131610 = 3.0;
        double r131611 = r131609 / r131610;
        double r131612 = r131608 - r131611;
        double r131613 = 9.0;
        double r131614 = r131613 * r131612;
        double r131615 = sqrt(r131614);
        double r131616 = r131609 / r131615;
        double r131617 = rand;
        double r131618 = r131616 * r131617;
        double r131619 = r131609 + r131618;
        double r131620 = r131612 * r131619;
        return r131620;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))