Average Error: 0.1 → 0.1
Time: 30.8s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{3}\]
\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) + rand \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{3}
double f(double a, double rand) {
        double r2200848 = a;
        double r2200849 = 1.0;
        double r2200850 = 3.0;
        double r2200851 = r2200849 / r2200850;
        double r2200852 = r2200848 - r2200851;
        double r2200853 = 1.0;
        double r2200854 = 9.0;
        double r2200855 = r2200854 * r2200852;
        double r2200856 = sqrt(r2200855);
        double r2200857 = r2200853 / r2200856;
        double r2200858 = rand;
        double r2200859 = r2200857 * r2200858;
        double r2200860 = r2200853 + r2200859;
        double r2200861 = r2200852 * r2200860;
        return r2200861;
}
↓
double f(double a, double rand) {
        double r2200862 = a;
        double r2200863 = 1.0;
        double r2200864 = 3.0;
        double r2200865 = r2200863 / r2200864;
        double r2200866 = r2200862 - r2200865;
        double r2200867 = rand;
        double r2200868 = sqrt(r2200866);
        double r2200869 = 3.0;
        double r2200870 = r2200868 / r2200869;
        double r2200871 = r2200867 * r2200870;
        double r2200872 = r2200866 + r2200871;
        return r2200872;
}

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

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

  6. Applied times-frac0.1

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

  7. Simplified0.1

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

  8. Simplified0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \left(\frac{\sqrt{a - \frac{1.0}{3.0}}}{3} \cdot \color{blue}{1}\right)\]

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019151 
(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))))