Average Error: 0.1 → 0.1
Time: 7.4s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(\left(a - \frac{1}{3}\right) \cdot \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot rand\]
\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(\left(a - \frac{1}{3}\right) \cdot \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot rand
double f(double a, double rand) {
        double r81510 = a;
        double r81511 = 1.0;
        double r81512 = 3.0;
        double r81513 = r81511 / r81512;
        double r81514 = r81510 - r81513;
        double r81515 = 9.0;
        double r81516 = r81515 * r81514;
        double r81517 = sqrt(r81516);
        double r81518 = r81511 / r81517;
        double r81519 = rand;
        double r81520 = r81518 * r81519;
        double r81521 = r81511 + r81520;
        double r81522 = r81514 * r81521;
        return r81522;
}
↓
double f(double a, double rand) {
        double r81523 = a;
        double r81524 = 1.0;
        double r81525 = 3.0;
        double r81526 = r81524 / r81525;
        double r81527 = r81523 - r81526;
        double r81528 = r81527 * r81524;
        double r81529 = 9.0;
        double r81530 = r81529 * r81527;
        double r81531 = sqrt(r81530);
        double r81532 = r81524 / r81531;
        double r81533 = r81527 * r81532;
        double r81534 = rand;
        double r81535 = r81533 * r81534;
        double r81536 = r81528 + r81535;
        return r81536;
}

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-*r*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020060 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))