Average Error: 0.1 → 0.1
Time: 19.6s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + {\left(9 \cdot \left(a - \frac{1.0}{3.0}\right)\right)}^{\frac{-1}{2}} \cdot rand\right)\]
\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(a - \frac{1.0}{3.0}\right) \cdot \left(1 + {\left(9 \cdot \left(a - \frac{1.0}{3.0}\right)\right)}^{\frac{-1}{2}} \cdot rand\right)
double f(double a, double rand) {
        double r1610606 = a;
        double r1610607 = 1.0;
        double r1610608 = 3.0;
        double r1610609 = r1610607 / r1610608;
        double r1610610 = r1610606 - r1610609;
        double r1610611 = 1.0;
        double r1610612 = 9.0;
        double r1610613 = r1610612 * r1610610;
        double r1610614 = sqrt(r1610613);
        double r1610615 = r1610611 / r1610614;
        double r1610616 = rand;
        double r1610617 = r1610615 * r1610616;
        double r1610618 = r1610611 + r1610617;
        double r1610619 = r1610610 * r1610618;
        return r1610619;
}
↓
double f(double a, double rand) {
        double r1610620 = a;
        double r1610621 = 1.0;
        double r1610622 = 3.0;
        double r1610623 = r1610621 / r1610622;
        double r1610624 = r1610620 - r1610623;
        double r1610625 = 1.0;
        double r1610626 = 9.0;
        double r1610627 = r1610626 * r1610624;
        double r1610628 = -0.5;
        double r1610629 = pow(r1610627, r1610628);
        double r1610630 = rand;
        double r1610631 = r1610629 * r1610630;
        double r1610632 = r1610625 + r1610631;
        double r1610633 = r1610624 * r1610632;
        return r1610633;
}

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 pow10.1

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

  4. Applied pow10.1

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

  5. Applied pow-prod-down0.1

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

  6. Applied sqrt-pow10.1

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

  7. Applied pow-flip0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019151 
(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))))