Average Error: 0.1 → 0.1
Time: 23.3s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\frac{a - \frac{1.0}{3.0}}{\sqrt{\left(a - \frac{1.0}{3.0}\right) \cdot 9}} \cdot rand + \left(a - \frac{1.0}{3.0}\right)\]
\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)
↓
\frac{a - \frac{1.0}{3.0}}{\sqrt{\left(a - \frac{1.0}{3.0}\right) \cdot 9}} \cdot rand + \left(a - \frac{1.0}{3.0}\right)
double f(double a, double rand) {
        double r2655912 = a;
        double r2655913 = 1.0;
        double r2655914 = 3.0;
        double r2655915 = r2655913 / r2655914;
        double r2655916 = r2655912 - r2655915;
        double r2655917 = 1.0;
        double r2655918 = 9.0;
        double r2655919 = r2655918 * r2655916;
        double r2655920 = sqrt(r2655919);
        double r2655921 = r2655917 / r2655920;
        double r2655922 = rand;
        double r2655923 = r2655921 * r2655922;
        double r2655924 = r2655917 + r2655923;
        double r2655925 = r2655916 * r2655924;
        return r2655925;
}
↓
double f(double a, double rand) {
        double r2655926 = a;
        double r2655927 = 1.0;
        double r2655928 = 3.0;
        double r2655929 = r2655927 / r2655928;
        double r2655930 = r2655926 - r2655929;
        double r2655931 = 9.0;
        double r2655932 = r2655930 * r2655931;
        double r2655933 = sqrt(r2655932);
        double r2655934 = r2655930 / r2655933;
        double r2655935 = rand;
        double r2655936 = r2655934 * r2655935;
        double r2655937 = r2655936 + r2655930;
        return r2655937;
}

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

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

  4. Applied div-inv0.1

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

  5. Applied associate-*l*0.1

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

  6. Simplified0.1

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

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

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

  9. Applied associate-*r*0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019130 
(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))))