Average Error: 0.1 → 0.1
Time: 6.4s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\]
\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 \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}
double f(double a, double rand) {
        double r64234 = a;
        double r64235 = 1.0;
        double r64236 = 3.0;
        double r64237 = r64235 / r64236;
        double r64238 = r64234 - r64237;
        double r64239 = 9.0;
        double r64240 = r64239 * r64238;
        double r64241 = sqrt(r64240);
        double r64242 = r64235 / r64241;
        double r64243 = rand;
        double r64244 = r64242 * r64243;
        double r64245 = r64235 + r64244;
        double r64246 = r64238 * r64245;
        return r64246;
}
↓
double f(double a, double rand) {
        double r64247 = a;
        double r64248 = 1.0;
        double r64249 = 3.0;
        double r64250 = r64248 / r64249;
        double r64251 = r64247 - r64250;
        double r64252 = r64251 * r64248;
        double r64253 = rand;
        double r64254 = r64248 * r64253;
        double r64255 = 9.0;
        double r64256 = r64255 * r64251;
        double r64257 = sqrt(r64256);
        double r64258 = r64254 / r64257;
        double r64259 = r64251 * r64258;
        double r64260 = r64252 + r64259;
        return r64260;
}

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 associate-*l/0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020056 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))