Average Error: 0.1 → 0.1
Time: 37.1s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) + \frac{rand}{\sqrt{3 \cdot \left(\left(a - \frac{1.0}{3.0}\right) \cdot 3\right)}} \cdot \left(a - \frac{1.0}{3.0}\right)\]
\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) + \frac{rand}{\sqrt{3 \cdot \left(\left(a - \frac{1.0}{3.0}\right) \cdot 3\right)}} \cdot \left(a - \frac{1.0}{3.0}\right)
double f(double a, double rand) {
        double r3555727 = a;
        double r3555728 = 1.0;
        double r3555729 = 3.0;
        double r3555730 = r3555728 / r3555729;
        double r3555731 = r3555727 - r3555730;
        double r3555732 = 1.0;
        double r3555733 = 9.0;
        double r3555734 = r3555733 * r3555731;
        double r3555735 = sqrt(r3555734);
        double r3555736 = r3555732 / r3555735;
        double r3555737 = rand;
        double r3555738 = r3555736 * r3555737;
        double r3555739 = r3555732 + r3555738;
        double r3555740 = r3555731 * r3555739;
        return r3555740;
}
↓
double f(double a, double rand) {
        double r3555741 = a;
        double r3555742 = 1.0;
        double r3555743 = 3.0;
        double r3555744 = r3555742 / r3555743;
        double r3555745 = r3555741 - r3555744;
        double r3555746 = rand;
        double r3555747 = 3.0;
        double r3555748 = r3555745 * r3555747;
        double r3555749 = r3555747 * r3555748;
        double r3555750 = sqrt(r3555749);
        double r3555751 = r3555746 / r3555750;
        double r3555752 = r3555751 * r3555745;
        double r3555753 = r3555745 + r3555752;
        return r3555753;
}

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. Using strategy rm

  3. Applied +-commutative0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \color{blue}{\left(\frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand + 1\right)}\]

  4. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{\left(a - \frac{1.0}{3.0}\right) \cdot \left(\frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right) + \left(a - \frac{1.0}{3.0}\right) \cdot 1}\]

  5. Simplified0.1

    \[\leadsto \color{blue}{\frac{rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot \left(a - \frac{1.0}{3.0}\right)} + \left(a - \frac{1.0}{3.0}\right) \cdot 1\]

  6. Simplified0.1

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

  8. Applied add-sqr-sqrt0.1

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

  9. Applied associate-*l*0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(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))))