Average Error: 0.1 → 0.1
Time: 9.1s
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 r112946 = a;
        double r112947 = 1.0;
        double r112948 = 3.0;
        double r112949 = r112947 / r112948;
        double r112950 = r112946 - r112949;
        double r112951 = 9.0;
        double r112952 = r112951 * r112950;
        double r112953 = sqrt(r112952);
        double r112954 = r112947 / r112953;
        double r112955 = rand;
        double r112956 = r112954 * r112955;
        double r112957 = r112947 + r112956;
        double r112958 = r112950 * r112957;
        return r112958;
}
↓
double f(double a, double rand) {
        double r112959 = a;
        double r112960 = 1.0;
        double r112961 = 3.0;
        double r112962 = r112960 / r112961;
        double r112963 = r112959 - r112962;
        double r112964 = 9.0;
        double r112965 = r112964 * r112963;
        double r112966 = sqrt(r112965);
        double r112967 = r112960 / r112966;
        double r112968 = rand;
        double r112969 = r112967 * r112968;
        double r112970 = r112960 + r112969;
        double r112971 = r112963 * r112970;
        return r112971;
}

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