Average Error: 0.1 → 0.1
Time: 32.9s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) + \left(\frac{\sqrt{a} + \sqrt{\frac{1.0}{3.0}}}{3} \cdot \frac{\sqrt{a} - \sqrt{\frac{1.0}{3.0}}}{\sqrt{a - \frac{1.0}{3.0}}}\right) \cdot rand\]
\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)
↓
\left(a - \frac{1.0}{3.0}\right) + \left(\frac{\sqrt{a} + \sqrt{\frac{1.0}{3.0}}}{3} \cdot \frac{\sqrt{a} - \sqrt{\frac{1.0}{3.0}}}{\sqrt{a - \frac{1.0}{3.0}}}\right) \cdot rand
double f(double a, double rand) {
        double r2321052 = a;
        double r2321053 = 1.0;
        double r2321054 = 3.0;
        double r2321055 = r2321053 / r2321054;
        double r2321056 = r2321052 - r2321055;
        double r2321057 = 1.0;
        double r2321058 = 9.0;
        double r2321059 = r2321058 * r2321056;
        double r2321060 = sqrt(r2321059);
        double r2321061 = r2321057 / r2321060;
        double r2321062 = rand;
        double r2321063 = r2321061 * r2321062;
        double r2321064 = r2321057 + r2321063;
        double r2321065 = r2321056 * r2321064;
        return r2321065;
}
↓
double f(double a, double rand) {
        double r2321066 = a;
        double r2321067 = 1.0;
        double r2321068 = 3.0;
        double r2321069 = r2321067 / r2321068;
        double r2321070 = r2321066 - r2321069;
        double r2321071 = sqrt(r2321066);
        double r2321072 = sqrt(r2321069);
        double r2321073 = r2321071 + r2321072;
        double r2321074 = 3.0;
        double r2321075 = r2321073 / r2321074;
        double r2321076 = r2321071 - r2321072;
        double r2321077 = sqrt(r2321070);
        double r2321078 = r2321076 / r2321077;
        double r2321079 = r2321075 * r2321078;
        double r2321080 = rand;
        double r2321081 = r2321079 * r2321080;
        double r2321082 = r2321070 + r2321081;
        return r2321082;
}

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

    \[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{a - \frac{1.0}{3.0}}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}}\]
  3. Using strategy rm

  4. Applied sqrt-prod0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{a - \frac{1.0}{3.0}}{\color{blue}{\sqrt{9} \cdot \sqrt{a - \frac{1.0}{3.0}}}}\]

  5. Applied add-sqr-sqrt0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{a - \color{blue}{\sqrt{\frac{1.0}{3.0}} \cdot \sqrt{\frac{1.0}{3.0}}}}{\sqrt{9} \cdot \sqrt{a - \frac{1.0}{3.0}}}\]

  6. Applied add-sqr-sqrt0.2

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{\color{blue}{\sqrt{a} \cdot \sqrt{a}} - \sqrt{\frac{1.0}{3.0}} \cdot \sqrt{\frac{1.0}{3.0}}}{\sqrt{9} \cdot \sqrt{a - \frac{1.0}{3.0}}}\]

  7. Applied difference-of-squares0.2

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{\color{blue}{\left(\sqrt{a} + \sqrt{\frac{1.0}{3.0}}\right) \cdot \left(\sqrt{a} - \sqrt{\frac{1.0}{3.0}}\right)}}{\sqrt{9} \cdot \sqrt{a - \frac{1.0}{3.0}}}\]

  8. Applied times-frac0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \color{blue}{\left(\frac{\sqrt{a} + \sqrt{\frac{1.0}{3.0}}}{\sqrt{9}} \cdot \frac{\sqrt{a} - \sqrt{\frac{1.0}{3.0}}}{\sqrt{a - \frac{1.0}{3.0}}}\right)}\]

  9. Simplified0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \left(\color{blue}{\frac{\sqrt{\frac{1.0}{3.0}} + \sqrt{a}}{3}} \cdot \frac{\sqrt{a} - \sqrt{\frac{1.0}{3.0}}}{\sqrt{a - \frac{1.0}{3.0}}}\right)\]

  10. Final simplification0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \left(\frac{\sqrt{a} + \sqrt{\frac{1.0}{3.0}}}{3} \cdot \frac{\sqrt{a} - \sqrt{\frac{1.0}{3.0}}}{\sqrt{a - \frac{1.0}{3.0}}}\right) \cdot rand\]

Reproduce

herbie shell --seed 2019142 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))))