Average Error: 0.1 → 0.1
Time: 6.9s
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 r81078 = a;
        double r81079 = 1.0;
        double r81080 = 3.0;
        double r81081 = r81079 / r81080;
        double r81082 = r81078 - r81081;
        double r81083 = 9.0;
        double r81084 = r81083 * r81082;
        double r81085 = sqrt(r81084);
        double r81086 = r81079 / r81085;
        double r81087 = rand;
        double r81088 = r81086 * r81087;
        double r81089 = r81079 + r81088;
        double r81090 = r81082 * r81089;
        return r81090;
}
↓
double f(double a, double rand) {
        double r81091 = a;
        double r81092 = 1.0;
        double r81093 = 3.0;
        double r81094 = r81092 / r81093;
        double r81095 = r81091 - r81094;
        double r81096 = r81095 * r81092;
        double r81097 = rand;
        double r81098 = r81092 * r81097;
        double r81099 = 9.0;
        double r81100 = r81099 * r81095;
        double r81101 = sqrt(r81100);
        double r81102 = r81098 / r81101;
        double r81103 = r81095 * r81102;
        double r81104 = r81096 + r81103;
        return r81104;
}

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 +o rules:numerics
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))