Average Error: 0.1 → 0.1
Time: 1.4m
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) + \sqrt{a - \frac{1.0}{3.0}} \cdot \left(\frac{\frac{rand}{3}}{\sqrt{a - \frac{1.0}{3.0}}} \cdot \sqrt{a - \frac{1.0}{3.0}}\right)\]
\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(a - \frac{1.0}{3.0}\right) + \sqrt{a - \frac{1.0}{3.0}} \cdot \left(\frac{\frac{rand}{3}}{\sqrt{a - \frac{1.0}{3.0}}} \cdot \sqrt{a - \frac{1.0}{3.0}}\right)
double f(double a, double rand) {
        double r2905600 = a;
        double r2905601 = 1.0;
        double r2905602 = 3.0;
        double r2905603 = r2905601 / r2905602;
        double r2905604 = r2905600 - r2905603;
        double r2905605 = 1.0;
        double r2905606 = 9.0;
        double r2905607 = r2905606 * r2905604;
        double r2905608 = sqrt(r2905607);
        double r2905609 = r2905605 / r2905608;
        double r2905610 = rand;
        double r2905611 = r2905609 * r2905610;
        double r2905612 = r2905605 + r2905611;
        double r2905613 = r2905604 * r2905612;
        return r2905613;
}
↓
double f(double a, double rand) {
        double r2905614 = a;
        double r2905615 = 1.0;
        double r2905616 = 3.0;
        double r2905617 = r2905615 / r2905616;
        double r2905618 = r2905614 - r2905617;
        double r2905619 = sqrt(r2905618);
        double r2905620 = rand;
        double r2905621 = 3.0;
        double r2905622 = r2905620 / r2905621;
        double r2905623 = r2905622 / r2905619;
        double r2905624 = r2905623 * r2905619;
        double r2905625 = r2905619 * r2905624;
        double r2905626 = r2905618 + r2905625;
        return r2905626;
}

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. Simplified0.1

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

  4. Applied sqrt-prod0.1

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

  5. Applied associate-/r*0.1

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

  6. Simplified0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \left(a - \frac{1.0}{3.0}\right) \cdot \frac{\color{blue}{\frac{rand}{3}}}{\sqrt{a - \frac{1.0}{3.0}}}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \color{blue}{\left(\sqrt{a - \frac{1.0}{3.0}} \cdot \sqrt{a - \frac{1.0}{3.0}}\right)} \cdot \frac{\frac{rand}{3}}{\sqrt{a - \frac{1.0}{3.0}}}\]

  9. Applied associate-*l*0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \color{blue}{\sqrt{a - \frac{1.0}{3.0}} \cdot \left(\sqrt{a - \frac{1.0}{3.0}} \cdot \frac{\frac{rand}{3}}{\sqrt{a - \frac{1.0}{3.0}}}\right)}\]

  10. Final simplification0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \sqrt{a - \frac{1.0}{3.0}} \cdot \left(\frac{\frac{rand}{3}}{\sqrt{a - \frac{1.0}{3.0}}} \cdot \sqrt{a - \frac{1.0}{3.0}}\right)\]

Reproduce

herbie shell --seed 2019153 
(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))))