Average Error: 0.1 → 0.1
Time: 32.3s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(\left(\frac{rand}{\sqrt{a - \frac{1}{3}}} \cdot 1\right) \cdot \frac{1}{\sqrt{9}} + 1\right) \cdot \left(a - \frac{1}{3}\right)\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\left(\left(\frac{rand}{\sqrt{a - \frac{1}{3}}} \cdot 1\right) \cdot \frac{1}{\sqrt{9}} + 1\right) \cdot \left(a - \frac{1}{3}\right)
double f(double a, double rand) {
        double r4825035 = a;
        double r4825036 = 1.0;
        double r4825037 = 3.0;
        double r4825038 = r4825036 / r4825037;
        double r4825039 = r4825035 - r4825038;
        double r4825040 = 9.0;
        double r4825041 = r4825040 * r4825039;
        double r4825042 = sqrt(r4825041);
        double r4825043 = r4825036 / r4825042;
        double r4825044 = rand;
        double r4825045 = r4825043 * r4825044;
        double r4825046 = r4825036 + r4825045;
        double r4825047 = r4825039 * r4825046;
        return r4825047;
}
↓
double f(double a, double rand) {
        double r4825048 = rand;
        double r4825049 = a;
        double r4825050 = 1.0;
        double r4825051 = 3.0;
        double r4825052 = r4825050 / r4825051;
        double r4825053 = r4825049 - r4825052;
        double r4825054 = sqrt(r4825053);
        double r4825055 = r4825048 / r4825054;
        double r4825056 = r4825055 * r4825050;
        double r4825057 = 1.0;
        double r4825058 = 9.0;
        double r4825059 = sqrt(r4825058);
        double r4825060 = r4825057 / r4825059;
        double r4825061 = r4825056 * r4825060;
        double r4825062 = r4825061 + r4825050;
        double r4825063 = r4825062 * r4825053;
        return r4825063;
}

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-prod0.1

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

  4. Applied *-un-lft-identity0.1

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

  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. Applied associate-*l*0.2

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

  8. Applied div-inv0.2

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

  9. Applied associate-*l*0.2

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019170 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))))