Average Error: 0.1 → 0.1
Time: 26.4s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{3}\]
\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) + rand \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{3}
double f(double a, double rand) {
        double r2245604 = a;
        double r2245605 = 1.0;
        double r2245606 = 3.0;
        double r2245607 = r2245605 / r2245606;
        double r2245608 = r2245604 - r2245607;
        double r2245609 = 1.0;
        double r2245610 = 9.0;
        double r2245611 = r2245610 * r2245608;
        double r2245612 = sqrt(r2245611);
        double r2245613 = r2245609 / r2245612;
        double r2245614 = rand;
        double r2245615 = r2245613 * r2245614;
        double r2245616 = r2245609 + r2245615;
        double r2245617 = r2245608 * r2245616;
        return r2245617;
}
↓
double f(double a, double rand) {
        double r2245618 = a;
        double r2245619 = 1.0;
        double r2245620 = 3.0;
        double r2245621 = r2245619 / r2245620;
        double r2245622 = r2245618 - r2245621;
        double r2245623 = rand;
        double r2245624 = sqrt(r2245622);
        double r2245625 = 3.0;
        double r2245626 = r2245624 / r2245625;
        double r2245627 = r2245623 * r2245626;
        double r2245628 = r2245622 + r2245627;
        return r2245628;
}

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

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

  4. Applied sqrt-prod0.1

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

  5. Applied add-sqr-sqrt0.1

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

  6. Applied times-frac0.1

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

  7. Simplified0.1

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

  8. Simplified0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \left(\frac{\sqrt{a - \frac{1.0}{3.0}}}{3} \cdot \color{blue}{1}\right)\]

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019152 
(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))))