Average Error: 0.1 → 0.1
Time: 7.5s
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 r81791 = a;
        double r81792 = 1.0;
        double r81793 = 3.0;
        double r81794 = r81792 / r81793;
        double r81795 = r81791 - r81794;
        double r81796 = 9.0;
        double r81797 = r81796 * r81795;
        double r81798 = sqrt(r81797);
        double r81799 = r81792 / r81798;
        double r81800 = rand;
        double r81801 = r81799 * r81800;
        double r81802 = r81792 + r81801;
        double r81803 = r81795 * r81802;
        return r81803;
}
↓
double f(double a, double rand) {
        double r81804 = a;
        double r81805 = 1.0;
        double r81806 = 3.0;
        double r81807 = r81805 / r81806;
        double r81808 = r81804 - r81807;
        double r81809 = 9.0;
        double r81810 = r81809 * r81808;
        double r81811 = sqrt(r81810);
        double r81812 = r81805 / r81811;
        double r81813 = rand;
        double r81814 = r81812 * r81813;
        double r81815 = r81805 + r81814;
        double r81816 = r81808 * r81815;
        return r81816;
}

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 2020021 +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))))