Average Error: 0.1 → 0.1
Time: 10.3s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
\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}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
double f(double a, double rand) {
        double r81939 = a;
        double r81940 = 1.0;
        double r81941 = 3.0;
        double r81942 = r81940 / r81941;
        double r81943 = r81939 - r81942;
        double r81944 = 9.0;
        double r81945 = r81944 * r81943;
        double r81946 = sqrt(r81945);
        double r81947 = r81940 / r81946;
        double r81948 = rand;
        double r81949 = r81947 * r81948;
        double r81950 = r81940 + r81949;
        double r81951 = r81943 * r81950;
        return r81951;
}
↓
double f(double a, double rand) {
        double r81952 = a;
        double r81953 = 1.0;
        double r81954 = 3.0;
        double r81955 = r81953 / r81954;
        double r81956 = r81952 - r81955;
        double r81957 = 9.0;
        double r81958 = r81957 * r81956;
        double r81959 = sqrt(r81958);
        double r81960 = r81953 / r81959;
        double r81961 = rand;
        double r81962 = r81960 * r81961;
        double r81963 = r81953 + r81962;
        double r81964 = r81956 * r81963;
        return r81964;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))