Average Error: 0.1 → 0.1
Time: 25.9s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[1 \cdot \left(a - \frac{1}{3}\right) + \left(1 \cdot rand\right) \cdot \frac{a - \frac{1}{3}}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
1 \cdot \left(a - \frac{1}{3}\right) + \left(1 \cdot rand\right) \cdot \frac{a - \frac{1}{3}}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}
double f(double a, double rand) {
        double r5797628 = a;
        double r5797629 = 1.0;
        double r5797630 = 3.0;
        double r5797631 = r5797629 / r5797630;
        double r5797632 = r5797628 - r5797631;
        double r5797633 = 9.0;
        double r5797634 = r5797633 * r5797632;
        double r5797635 = sqrt(r5797634);
        double r5797636 = r5797629 / r5797635;
        double r5797637 = rand;
        double r5797638 = r5797636 * r5797637;
        double r5797639 = r5797629 + r5797638;
        double r5797640 = r5797632 * r5797639;
        return r5797640;
}
↓
double f(double a, double rand) {
        double r5797641 = 1.0;
        double r5797642 = a;
        double r5797643 = 3.0;
        double r5797644 = r5797641 / r5797643;
        double r5797645 = r5797642 - r5797644;
        double r5797646 = r5797641 * r5797645;
        double r5797647 = rand;
        double r5797648 = r5797641 * r5797647;
        double r5797649 = 9.0;
        double r5797650 = r5797649 * r5797645;
        double r5797651 = sqrt(r5797650);
        double r5797652 = r5797645 / r5797651;
        double r5797653 = r5797648 * r5797652;
        double r5797654 = r5797646 + r5797653;
        return r5797654;
}

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-rgt-in0.1

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

  5. Applied associate-*l/0.1

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

  7. Applied div-inv0.1

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

  8. Applied associate-*l*0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))))