Average Error: 0.2 → 0.1
Time: 1.6m
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\frac{a - \frac{1.0}{3.0}}{\sqrt{\left(\left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(a - \frac{1.0}{3.0}\right)\right) \cdot \sqrt[3]{9}}} \cdot rand + \left(a - \frac{1.0}{3.0}\right)\]
\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)
↓
\frac{a - \frac{1.0}{3.0}}{\sqrt{\left(\left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(a - \frac{1.0}{3.0}\right)\right) \cdot \sqrt[3]{9}}} \cdot rand + \left(a - \frac{1.0}{3.0}\right)
double f(double a, double rand) {
        double r6394827 = a;
        double r6394828 = 1.0;
        double r6394829 = 3.0;
        double r6394830 = r6394828 / r6394829;
        double r6394831 = r6394827 - r6394830;
        double r6394832 = 1.0;
        double r6394833 = 9.0;
        double r6394834 = r6394833 * r6394831;
        double r6394835 = sqrt(r6394834);
        double r6394836 = r6394832 / r6394835;
        double r6394837 = rand;
        double r6394838 = r6394836 * r6394837;
        double r6394839 = r6394832 + r6394838;
        double r6394840 = r6394831 * r6394839;
        return r6394840;
}
↓
double f(double a, double rand) {
        double r6394841 = a;
        double r6394842 = 1.0;
        double r6394843 = 3.0;
        double r6394844 = r6394842 / r6394843;
        double r6394845 = r6394841 - r6394844;
        double r6394846 = 9.0;
        double r6394847 = cbrt(r6394846);
        double r6394848 = r6394847 * r6394847;
        double r6394849 = r6394848 * r6394845;
        double r6394850 = r6394849 * r6394847;
        double r6394851 = sqrt(r6394850);
        double r6394852 = r6394845 / r6394851;
        double r6394853 = rand;
        double r6394854 = r6394852 * r6394853;
        double r6394855 = r6394854 + r6394845;
        return r6394855;
}

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 0.2

    \[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{rand \cdot \frac{a - \frac{1.0}{3.0}}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} + \left(a - \frac{1.0}{3.0}\right)}\]
  3. Using strategy rm

  4. Applied *-commutative0.1

    \[\leadsto rand \cdot \frac{a - \frac{1.0}{3.0}}{\sqrt{\color{blue}{\left(a - \frac{1.0}{3.0}\right) \cdot 9}}} + \left(a - \frac{1.0}{3.0}\right)\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.1

    \[\leadsto rand \cdot \frac{a - \frac{1.0}{3.0}}{\sqrt{\left(a - \frac{1.0}{3.0}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \sqrt[3]{9}\right)}}} + \left(a - \frac{1.0}{3.0}\right)\]

  7. Applied associate-*r*0.1

    \[\leadsto rand \cdot \frac{a - \frac{1.0}{3.0}}{\sqrt{\color{blue}{\left(\left(a - \frac{1.0}{3.0}\right) \cdot \left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right)\right) \cdot \sqrt[3]{9}}}} + \left(a - \frac{1.0}{3.0}\right)\]

  8. Final simplification0.1

    \[\leadsto \frac{a - \frac{1.0}{3.0}}{\sqrt{\left(\left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(a - \frac{1.0}{3.0}\right)\right) \cdot \sqrt[3]{9}}} \cdot rand + \left(a - \frac{1.0}{3.0}\right)\]

Reproduce

herbie shell --seed 2019107 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))))