Average Error: 0.1 → 0.1
Time: 6.2s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}}\right)\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}}\right)
double f(double a, double rand) {
        double r75940 = a;
        double r75941 = 1.0;
        double r75942 = 3.0;
        double r75943 = r75941 / r75942;
        double r75944 = r75940 - r75943;
        double r75945 = 9.0;
        double r75946 = r75945 * r75944;
        double r75947 = sqrt(r75946);
        double r75948 = r75941 / r75947;
        double r75949 = rand;
        double r75950 = r75948 * r75949;
        double r75951 = r75941 + r75950;
        double r75952 = r75944 * r75951;
        return r75952;
}
↓
double f(double a, double rand) {
        double r75953 = a;
        double r75954 = 1.0;
        double r75955 = 3.0;
        double r75956 = r75954 / r75955;
        double r75957 = r75953 - r75956;
        double r75958 = rand;
        double r75959 = r75954 * r75958;
        double r75960 = 9.0;
        double r75961 = sqrt(r75960);
        double r75962 = sqrt(r75957);
        double r75963 = r75961 * r75962;
        double r75964 = r75959 / r75963;
        double r75965 = r75954 + r75964;
        double r75966 = r75957 * r75965;
        return r75966;
}

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 associate-*l/0.1

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

  5. Applied sqrt-prod0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020059 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))