Average Error: 0.1 → 0.1
Time: 6.7s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\frac{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}{rand}}\right)\]
\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}{\frac{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}{rand}}\right)
double f(double a, double rand) {
        double r84147 = a;
        double r84148 = 1.0;
        double r84149 = 3.0;
        double r84150 = r84148 / r84149;
        double r84151 = r84147 - r84150;
        double r84152 = 9.0;
        double r84153 = r84152 * r84151;
        double r84154 = sqrt(r84153);
        double r84155 = r84148 / r84154;
        double r84156 = rand;
        double r84157 = r84155 * r84156;
        double r84158 = r84148 + r84157;
        double r84159 = r84151 * r84158;
        return r84159;
}
↓
double f(double a, double rand) {
        double r84160 = a;
        double r84161 = 1.0;
        double r84162 = 3.0;
        double r84163 = r84161 / r84162;
        double r84164 = r84160 - r84163;
        double r84165 = 9.0;
        double r84166 = r84165 * r84164;
        double r84167 = sqrt(r84166);
        double r84168 = rand;
        double r84169 = r84167 / r84168;
        double r84170 = r84161 / r84169;
        double r84171 = r84161 + r84170;
        double r84172 = r84164 * r84171;
        return r84172;
}

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 associate-/l*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020049 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))