Average Error: 0.1 → 0.1
Time: 21.6s
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 r3649135 = a;
        double r3649136 = 1.0;
        double r3649137 = 3.0;
        double r3649138 = r3649136 / r3649137;
        double r3649139 = r3649135 - r3649138;
        double r3649140 = 1.0;
        double r3649141 = 9.0;
        double r3649142 = r3649141 * r3649139;
        double r3649143 = sqrt(r3649142);
        double r3649144 = r3649140 / r3649143;
        double r3649145 = rand;
        double r3649146 = r3649144 * r3649145;
        double r3649147 = r3649140 + r3649146;
        double r3649148 = r3649139 * r3649147;
        return r3649148;
}
↓
double f(double a, double rand) {
        double r3649149 = a;
        double r3649150 = 1.0;
        double r3649151 = 3.0;
        double r3649152 = r3649150 / r3649151;
        double r3649153 = r3649149 - r3649152;
        double r3649154 = rand;
        double r3649155 = 9.0;
        double r3649156 = r3649155 * r3649153;
        double r3649157 = sqrt(r3649156);
        double r3649158 = r3649154 / r3649157;
        double r3649159 = r3649153 * r3649158;
        double r3649160 = r3649159 + r3649153;
        return r3649160;
}

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 distribute-lft-in0.1

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

  4. Simplified0.1

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

  5. Simplified0.1

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

  6. 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 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))))