Average Error: 0.1 → 0.1
Time: 7.1s
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 r75167 = a;
        double r75168 = 1.0;
        double r75169 = 3.0;
        double r75170 = r75168 / r75169;
        double r75171 = r75167 - r75170;
        double r75172 = 9.0;
        double r75173 = r75172 * r75171;
        double r75174 = sqrt(r75173);
        double r75175 = r75168 / r75174;
        double r75176 = rand;
        double r75177 = r75175 * r75176;
        double r75178 = r75168 + r75177;
        double r75179 = r75171 * r75178;
        return r75179;
}
↓
double f(double a, double rand) {
        double r75180 = a;
        double r75181 = 1.0;
        double r75182 = 3.0;
        double r75183 = r75181 / r75182;
        double r75184 = r75180 - r75183;
        double r75185 = rand;
        double r75186 = r75181 * r75185;
        double r75187 = 9.0;
        double r75188 = r75187 * r75184;
        double r75189 = sqrt(r75188);
        double r75190 = r75186 / r75189;
        double r75191 = r75181 + r75190;
        double r75192 = r75184 * r75191;
        return r75192;
}

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. 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 2019353 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))