Average Error: 0.1 → 0.1
Time: 25.6s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} + \left(a - \frac{1.0}{3.0}\right)\]
\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)
↓
\left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} + \left(a - \frac{1.0}{3.0}\right)
double f(double a, double rand) {
        double r3187935 = a;
        double r3187936 = 1.0;
        double r3187937 = 3.0;
        double r3187938 = r3187936 / r3187937;
        double r3187939 = r3187935 - r3187938;
        double r3187940 = 1.0;
        double r3187941 = 9.0;
        double r3187942 = r3187941 * r3187939;
        double r3187943 = sqrt(r3187942);
        double r3187944 = r3187940 / r3187943;
        double r3187945 = rand;
        double r3187946 = r3187944 * r3187945;
        double r3187947 = r3187940 + r3187946;
        double r3187948 = r3187939 * r3187947;
        return r3187948;
}
↓
double f(double a, double rand) {
        double r3187949 = a;
        double r3187950 = 1.0;
        double r3187951 = 3.0;
        double r3187952 = r3187950 / r3187951;
        double r3187953 = r3187949 - r3187952;
        double r3187954 = rand;
        double r3187955 = 9.0;
        double r3187956 = r3187955 * r3187953;
        double r3187957 = sqrt(r3187956);
        double r3187958 = r3187954 / r3187957;
        double r3187959 = r3187953 * r3187958;
        double r3187960 = r3187959 + r3187953;
        return r3187960;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.1

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

  4. Simplified0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(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))))