Average Error: 0.1 → 0.1
Time: 8.7s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{\frac{1 \cdot rand}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}}\right)\]
\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{\frac{1 \cdot rand}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}}\right)
double f(double a, double rand) {
        double r80986 = a;
        double r80987 = 1.0;
        double r80988 = 3.0;
        double r80989 = r80987 / r80988;
        double r80990 = r80986 - r80989;
        double r80991 = 9.0;
        double r80992 = r80991 * r80990;
        double r80993 = sqrt(r80992);
        double r80994 = r80987 / r80993;
        double r80995 = rand;
        double r80996 = r80994 * r80995;
        double r80997 = r80987 + r80996;
        double r80998 = r80990 * r80997;
        return r80998;
}
↓
double f(double a, double rand) {
        double r80999 = a;
        double r81000 = 1.0;
        double r81001 = 3.0;
        double r81002 = r81000 / r81001;
        double r81003 = r80999 - r81002;
        double r81004 = rand;
        double r81005 = r81000 * r81004;
        double r81006 = 9.0;
        double r81007 = sqrt(r81006);
        double r81008 = r81005 / r81007;
        double r81009 = sqrt(r81003);
        double r81010 = r81008 / r81009;
        double r81011 = r81000 + r81010;
        double r81012 = r81003 * r81011;
        return r81012;
}

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 sqrt-prod0.2

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

  4. Applied *-un-lft-identity0.2

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

  5. Applied times-frac0.2

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

  6. Applied associate-*l*0.2

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

  8. Applied associate-*l/0.2

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

  9. Applied associate-*r/0.2

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020089 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))