Average Error: 0.1 → 0.1
Time: 20.6s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right)\]
\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 \left(1 + \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right)
double f(double a, double rand) {
        double r80092 = a;
        double r80093 = 1.0;
        double r80094 = 3.0;
        double r80095 = r80093 / r80094;
        double r80096 = r80092 - r80095;
        double r80097 = 9.0;
        double r80098 = r80097 * r80096;
        double r80099 = sqrt(r80098);
        double r80100 = r80093 / r80099;
        double r80101 = rand;
        double r80102 = r80100 * r80101;
        double r80103 = r80093 + r80102;
        double r80104 = r80096 * r80103;
        return r80104;
}
↓
double f(double a, double rand) {
        double r80105 = a;
        double r80106 = 1.0;
        double r80107 = 3.0;
        double r80108 = r80106 / r80107;
        double r80109 = r80105 - r80108;
        double r80110 = rand;
        double r80111 = r80106 * r80110;
        double r80112 = 9.0;
        double r80113 = r80112 * r80109;
        double r80114 = sqrt(r80113);
        double r80115 = r80111 / r80114;
        double r80116 = r80106 + r80115;
        double r80117 = r80109 * r80116;
        return r80117;
}

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 associate-*l/0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019294 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))