Average Error: 0.1 → 0.2
Time: 45.6s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \left(\frac{1}{\sqrt{9}} \cdot \frac{1}{\sqrt{a - \frac{1}{3}}}\right) \cdot rand\right)\]
\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 + \left(\frac{1}{\sqrt{9}} \cdot \frac{1}{\sqrt{a - \frac{1}{3}}}\right) \cdot rand\right)
double f(double a, double rand) {
        double r231241 = a;
        double r231242 = 1.0;
        double r231243 = 3.0;
        double r231244 = r231242 / r231243;
        double r231245 = r231241 - r231244;
        double r231246 = 9.0;
        double r231247 = r231246 * r231245;
        double r231248 = sqrt(r231247);
        double r231249 = r231242 / r231248;
        double r231250 = rand;
        double r231251 = r231249 * r231250;
        double r231252 = r231242 + r231251;
        double r231253 = r231245 * r231252;
        return r231253;
}
↓
double f(double a, double rand) {
        double r231254 = a;
        double r231255 = 1.0;
        double r231256 = 3.0;
        double r231257 = r231255 / r231256;
        double r231258 = r231254 - r231257;
        double r231259 = 1.0;
        double r231260 = 9.0;
        double r231261 = sqrt(r231260);
        double r231262 = r231259 / r231261;
        double r231263 = sqrt(r231258);
        double r231264 = r231255 / r231263;
        double r231265 = r231262 * r231264;
        double r231266 = rand;
        double r231267 = r231265 * r231266;
        double r231268 = r231255 + r231267;
        double r231269 = r231258 * r231268;
        return r231269;
}

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 sqrt-prod0.2

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

  4. Applied *-un-lft-identity0.2

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

  5. Applied times-frac0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020045 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))