Average Error: 0.1 → 0.1
Time: 1.4m
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right)\]
\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 \left(a - \frac{1}{3}\right)}}\right)
double f(double a, double rand) {
        double r235792 = a;
        double r235793 = 1.0;
        double r235794 = 3.0;
        double r235795 = r235793 / r235794;
        double r235796 = r235792 - r235795;
        double r235797 = 9.0;
        double r235798 = r235797 * r235796;
        double r235799 = sqrt(r235798);
        double r235800 = r235793 / r235799;
        double r235801 = rand;
        double r235802 = r235800 * r235801;
        double r235803 = r235793 + r235802;
        double r235804 = r235796 * r235803;
        return r235804;
}
↓
double f(double a, double rand) {
        double r235805 = a;
        double r235806 = 1.0;
        double r235807 = 3.0;
        double r235808 = r235806 / r235807;
        double r235809 = r235805 - r235808;
        double r235810 = rand;
        double r235811 = r235806 * r235810;
        double r235812 = 9.0;
        double r235813 = r235812 * r235809;
        double r235814 = sqrt(r235813);
        double r235815 = r235811 / r235814;
        double r235816 = r235806 + r235815;
        double r235817 = r235809 * r235816;
        return r235817;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))