Average Error: 0.1 → 0.1
Time: 22.8s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) + \left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand \cdot \frac{1}{3}}{\sqrt{a - \frac{1.0}{3.0}}}\]
\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) + \left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand \cdot \frac{1}{3}}{\sqrt{a - \frac{1.0}{3.0}}}
double f(double a, double rand) {
        double r3579732 = a;
        double r3579733 = 1.0;
        double r3579734 = 3.0;
        double r3579735 = r3579733 / r3579734;
        double r3579736 = r3579732 - r3579735;
        double r3579737 = 1.0;
        double r3579738 = 9.0;
        double r3579739 = r3579738 * r3579736;
        double r3579740 = sqrt(r3579739);
        double r3579741 = r3579737 / r3579740;
        double r3579742 = rand;
        double r3579743 = r3579741 * r3579742;
        double r3579744 = r3579737 + r3579743;
        double r3579745 = r3579736 * r3579744;
        return r3579745;
}
↓
double f(double a, double rand) {
        double r3579746 = a;
        double r3579747 = 1.0;
        double r3579748 = 3.0;
        double r3579749 = r3579747 / r3579748;
        double r3579750 = r3579746 - r3579749;
        double r3579751 = rand;
        double r3579752 = 0.3333333333333333;
        double r3579753 = r3579751 * r3579752;
        double r3579754 = sqrt(r3579750);
        double r3579755 = r3579753 / r3579754;
        double r3579756 = r3579750 * r3579755;
        double r3579757 = r3579750 + r3579756;
        return r3579757;
}

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 sqrt-prod0.1

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

  4. Simplified0.1

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

  6. Applied *-un-lft-identity0.1

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

  7. Applied associate-*l*0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(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))))