Average Error: 0.1 → 0.1
Time: 24.7s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(\left(a - \frac{1.0}{3.0}\right) \cdot {\left(\left(a - \frac{1.0}{3.0}\right) \cdot 9\right)}^{\left(-\frac{1}{2}\right)}\right) \cdot rand + \left(a - \frac{1.0}{3.0}\right)\]
\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)
↓
\left(\left(a - \frac{1.0}{3.0}\right) \cdot {\left(\left(a - \frac{1.0}{3.0}\right) \cdot 9\right)}^{\left(-\frac{1}{2}\right)}\right) \cdot rand + \left(a - \frac{1.0}{3.0}\right)
double f(double a, double rand) {
        double r2491467 = a;
        double r2491468 = 1.0;
        double r2491469 = 3.0;
        double r2491470 = r2491468 / r2491469;
        double r2491471 = r2491467 - r2491470;
        double r2491472 = 1.0;
        double r2491473 = 9.0;
        double r2491474 = r2491473 * r2491471;
        double r2491475 = sqrt(r2491474);
        double r2491476 = r2491472 / r2491475;
        double r2491477 = rand;
        double r2491478 = r2491476 * r2491477;
        double r2491479 = r2491472 + r2491478;
        double r2491480 = r2491471 * r2491479;
        return r2491480;
}
↓
double f(double a, double rand) {
        double r2491481 = a;
        double r2491482 = 1.0;
        double r2491483 = 3.0;
        double r2491484 = r2491482 / r2491483;
        double r2491485 = r2491481 - r2491484;
        double r2491486 = 9.0;
        double r2491487 = r2491485 * r2491486;
        double r2491488 = 0.5;
        double r2491489 = -r2491488;
        double r2491490 = pow(r2491487, r2491489);
        double r2491491 = r2491485 * r2491490;
        double r2491492 = rand;
        double r2491493 = r2491491 * r2491492;
        double r2491494 = r2491493 + r2491485;
        return r2491494;
}

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. Using strategy rm

  3. Applied pow1/20.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\color{blue}{{\left(9 \cdot \left(a - \frac{1.0}{3.0}\right)\right)}^{\frac{1}{2}}}} \cdot rand\right)\]

  4. Applied pow-flip0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \color{blue}{{\left(9 \cdot \left(a - \frac{1.0}{3.0}\right)\right)}^{\left(-\frac{1}{2}\right)}} \cdot rand\right)\]
  5. Using strategy rm

  6. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{\left(a - \frac{1.0}{3.0}\right) \cdot 1 + \left(a - \frac{1.0}{3.0}\right) \cdot \left({\left(9 \cdot \left(a - \frac{1.0}{3.0}\right)\right)}^{\left(-\frac{1}{2}\right)} \cdot rand\right)}\]

  7. Simplified0.1

    \[\leadsto \color{blue}{\left(a - \frac{1.0}{3.0}\right)} + \left(a - \frac{1.0}{3.0}\right) \cdot \left({\left(9 \cdot \left(a - \frac{1.0}{3.0}\right)\right)}^{\left(-\frac{1}{2}\right)} \cdot rand\right)\]
  8. Using strategy rm

  9. Applied associate-*r*0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \color{blue}{\left(\left(a - \frac{1.0}{3.0}\right) \cdot {\left(9 \cdot \left(a - \frac{1.0}{3.0}\right)\right)}^{\left(-\frac{1}{2}\right)}\right) \cdot rand}\]

  10. Final simplification0.1

    \[\leadsto \left(\left(a - \frac{1.0}{3.0}\right) \cdot {\left(\left(a - \frac{1.0}{3.0}\right) \cdot 9\right)}^{\left(-\frac{1}{2}\right)}\right) \cdot rand + \left(a - \frac{1.0}{3.0}\right)\]

Reproduce

herbie shell --seed 2019134 
(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))))