Average Error: 0.1 → 0.1
Time: 1.4m
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} + \left(a - \frac{1.0}{3.0}\right)\]
\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) \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} + \left(a - \frac{1.0}{3.0}\right)
double f(double a, double rand) {
        double r3460736 = a;
        double r3460737 = 1.0;
        double r3460738 = 3.0;
        double r3460739 = r3460737 / r3460738;
        double r3460740 = r3460736 - r3460739;
        double r3460741 = 1.0;
        double r3460742 = 9.0;
        double r3460743 = r3460742 * r3460740;
        double r3460744 = sqrt(r3460743);
        double r3460745 = r3460741 / r3460744;
        double r3460746 = rand;
        double r3460747 = r3460745 * r3460746;
        double r3460748 = r3460741 + r3460747;
        double r3460749 = r3460740 * r3460748;
        return r3460749;
}
↓
double f(double a, double rand) {
        double r3460750 = a;
        double r3460751 = 1.0;
        double r3460752 = 3.0;
        double r3460753 = r3460751 / r3460752;
        double r3460754 = r3460750 - r3460753;
        double r3460755 = rand;
        double r3460756 = 9.0;
        double r3460757 = r3460756 * r3460754;
        double r3460758 = sqrt(r3460757);
        double r3460759 = r3460755 / r3460758;
        double r3460760 = r3460754 * r3460759;
        double r3460761 = r3460760 + r3460754;
        return r3460761;
}

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. Simplified0.1

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

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

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

  5. Applied associate-*r*0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019135 
(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))))