Average Error: 0.1 → 0.1
Time: 24.8s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \frac{\frac{1}{\sqrt{9}} \cdot rand}{\sqrt{a - \frac{1}{3}}} \cdot \left(a - \frac{1}{3}\right)\]
\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 1 + \frac{\frac{1}{\sqrt{9}} \cdot rand}{\sqrt{a - \frac{1}{3}}} \cdot \left(a - \frac{1}{3}\right)
double f(double a, double rand) {
        double r77056 = a;
        double r77057 = 1.0;
        double r77058 = 3.0;
        double r77059 = r77057 / r77058;
        double r77060 = r77056 - r77059;
        double r77061 = 9.0;
        double r77062 = r77061 * r77060;
        double r77063 = sqrt(r77062);
        double r77064 = r77057 / r77063;
        double r77065 = rand;
        double r77066 = r77064 * r77065;
        double r77067 = r77057 + r77066;
        double r77068 = r77060 * r77067;
        return r77068;
}
↓
double f(double a, double rand) {
        double r77069 = a;
        double r77070 = 1.0;
        double r77071 = 3.0;
        double r77072 = r77070 / r77071;
        double r77073 = r77069 - r77072;
        double r77074 = r77073 * r77070;
        double r77075 = 9.0;
        double r77076 = sqrt(r77075);
        double r77077 = r77070 / r77076;
        double r77078 = rand;
        double r77079 = r77077 * r77078;
        double r77080 = sqrt(r77073);
        double r77081 = r77079 / r77080;
        double r77082 = r77081 * r77073;
        double r77083 = r77074 + r77082;
        return r77083;
}

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. Simplified0.1

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

  6. Applied sqrt-prod0.1

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

  7. Applied associate-/r*0.1

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

  9. Applied associate-*l/0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019208 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))