Average Error: 0.1 → 0.1
Time: 6.8s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \frac{1}{\frac{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}{\left(a - \frac{1}{3}\right) \cdot 1}} \cdot rand\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\left(a - \frac{1}{3}\right) \cdot 1 + \frac{1}{\frac{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}{\left(a - \frac{1}{3}\right) \cdot 1}} \cdot rand
double f(double a, double rand) {
        double r141620 = a;
        double r141621 = 1.0;
        double r141622 = 3.0;
        double r141623 = r141621 / r141622;
        double r141624 = r141620 - r141623;
        double r141625 = 9.0;
        double r141626 = r141625 * r141624;
        double r141627 = sqrt(r141626);
        double r141628 = r141621 / r141627;
        double r141629 = rand;
        double r141630 = r141628 * r141629;
        double r141631 = r141621 + r141630;
        double r141632 = r141624 * r141631;
        return r141632;
}
↓
double f(double a, double rand) {
        double r141633 = a;
        double r141634 = 1.0;
        double r141635 = 3.0;
        double r141636 = r141634 / r141635;
        double r141637 = r141633 - r141636;
        double r141638 = r141637 * r141634;
        double r141639 = 1.0;
        double r141640 = 9.0;
        double r141641 = r141640 * r141637;
        double r141642 = sqrt(r141641);
        double r141643 = r141642 / r141638;
        double r141644 = r141639 / r141643;
        double r141645 = rand;
        double r141646 = r141644 * r141645;
        double r141647 = r141638 + r141646;
        return r141647;
}

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-lft-in0.1

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

  5. Applied associate-*r*0.1

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

  7. Applied associate-*r/0.1

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

  9. Applied clear-num0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020039 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))