Average Error: 0.1 → 0.1
Time: 8.7s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \left(1 \cdot \frac{\frac{rand}{\sqrt{a - \frac{1}{3}}}}{\sqrt{9}}\right)\]
\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 + \left(a - \frac{1}{3}\right) \cdot \left(1 \cdot \frac{\frac{rand}{\sqrt{a - \frac{1}{3}}}}{\sqrt{9}}\right)
double f(double a, double rand) {
        double r95678 = a;
        double r95679 = 1.0;
        double r95680 = 3.0;
        double r95681 = r95679 / r95680;
        double r95682 = r95678 - r95681;
        double r95683 = 9.0;
        double r95684 = r95683 * r95682;
        double r95685 = sqrt(r95684);
        double r95686 = r95679 / r95685;
        double r95687 = rand;
        double r95688 = r95686 * r95687;
        double r95689 = r95679 + r95688;
        double r95690 = r95682 * r95689;
        return r95690;
}
↓
double f(double a, double rand) {
        double r95691 = a;
        double r95692 = 1.0;
        double r95693 = 3.0;
        double r95694 = r95692 / r95693;
        double r95695 = r95691 - r95694;
        double r95696 = r95695 * r95692;
        double r95697 = rand;
        double r95698 = sqrt(r95695);
        double r95699 = r95697 / r95698;
        double r95700 = 9.0;
        double r95701 = sqrt(r95700);
        double r95702 = r95699 / r95701;
        double r95703 = r95692 * r95702;
        double r95704 = r95695 * r95703;
        double r95705 = r95696 + r95704;
        return r95705;
}

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 sqrt-prod0.1

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

  7. Applied div-inv0.1

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

  8. Applied associate-*l*0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020033 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))