Average Error: 0.1 → 0.1
Time: 7.3s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(\left(a - \frac{1}{3}\right) \cdot \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot rand\]
\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 1 + \left(\left(a - \frac{1}{3}\right) \cdot \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot rand
double f(double a, double rand) {
        double r77814 = a;
        double r77815 = 1.0;
        double r77816 = 3.0;
        double r77817 = r77815 / r77816;
        double r77818 = r77814 - r77817;
        double r77819 = 9.0;
        double r77820 = r77819 * r77818;
        double r77821 = sqrt(r77820);
        double r77822 = r77815 / r77821;
        double r77823 = rand;
        double r77824 = r77822 * r77823;
        double r77825 = r77815 + r77824;
        double r77826 = r77818 * r77825;
        return r77826;
}
↓
double f(double a, double rand) {
        double r77827 = a;
        double r77828 = 1.0;
        double r77829 = 3.0;
        double r77830 = r77828 / r77829;
        double r77831 = r77827 - r77830;
        double r77832 = r77831 * r77828;
        double r77833 = 9.0;
        double r77834 = r77833 * r77831;
        double r77835 = sqrt(r77834);
        double r77836 = r77828 / r77835;
        double r77837 = r77831 * r77836;
        double r77838 = rand;
        double r77839 = r77837 * r77838;
        double r77840 = r77832 + r77839;
        return r77840;
}

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 distribute-lft-in0.1

    \[\leadsto \color{blue}{\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \left(\frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)}\]
  4. Using strategy rm

  5. Applied associate-*r*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))