Average Error: 0.1 → 0.2
Time: 56.0s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1.0 + \frac{1.0}{\sqrt{9.0 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(\frac{\frac{1.0}{\sqrt{9.0}} \cdot rand}{\sqrt{a - \frac{1.0}{3.0}}} + 1.0\right)\]
\left(a - \frac{1.0}{3.0}\right) \cdot \left(1.0 + \frac{1.0}{\sqrt{9.0 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)
↓
\left(a - \frac{1.0}{3.0}\right) \cdot \left(\frac{\frac{1.0}{\sqrt{9.0}} \cdot rand}{\sqrt{a - \frac{1.0}{3.0}}} + 1.0\right)
double f(double a, double rand) {
        double r3234050 = a;
        double r3234051 = 1.0;
        double r3234052 = 3.0;
        double r3234053 = r3234051 / r3234052;
        double r3234054 = r3234050 - r3234053;
        double r3234055 = 9.0;
        double r3234056 = r3234055 * r3234054;
        double r3234057 = sqrt(r3234056);
        double r3234058 = r3234051 / r3234057;
        double r3234059 = rand;
        double r3234060 = r3234058 * r3234059;
        double r3234061 = r3234051 + r3234060;
        double r3234062 = r3234054 * r3234061;
        return r3234062;
}
↓
double f(double a, double rand) {
        double r3234063 = a;
        double r3234064 = 1.0;
        double r3234065 = 3.0;
        double r3234066 = r3234064 / r3234065;
        double r3234067 = r3234063 - r3234066;
        double r3234068 = 9.0;
        double r3234069 = sqrt(r3234068);
        double r3234070 = r3234064 / r3234069;
        double r3234071 = rand;
        double r3234072 = r3234070 * r3234071;
        double r3234073 = sqrt(r3234067);
        double r3234074 = r3234072 / r3234073;
        double r3234075 = r3234074 + r3234064;
        double r3234076 = r3234067 * r3234075;
        return r3234076;
}

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

    \[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1.0 + \frac{1.0}{\sqrt{9.0 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
  2. Using strategy rm

  3. Applied sqrt-prod0.2

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1.0 + \frac{1.0}{\color{blue}{\sqrt{9.0} \cdot \sqrt{a - \frac{1.0}{3.0}}}} \cdot rand\right)\]

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

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1.0 + \frac{\color{blue}{1 \cdot 1.0}}{\sqrt{9.0} \cdot \sqrt{a - \frac{1.0}{3.0}}} \cdot rand\right)\]

  5. Applied times-frac0.2

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1.0 + \color{blue}{\left(\frac{1}{\sqrt{9.0}} \cdot \frac{1.0}{\sqrt{a - \frac{1.0}{3.0}}}\right)} \cdot rand\right)\]
  6. Using strategy rm

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

    \[\leadsto \color{blue}{\left(1 \cdot \left(a - \frac{1.0}{3.0}\right)\right)} \cdot \left(1.0 + \left(\frac{1}{\sqrt{9.0}} \cdot \frac{1.0}{\sqrt{a - \frac{1.0}{3.0}}}\right) \cdot rand\right)\]

  8. Applied associate-*l*0.2

    \[\leadsto \color{blue}{1 \cdot \left(\left(a - \frac{1.0}{3.0}\right) \cdot \left(1.0 + \left(\frac{1}{\sqrt{9.0}} \cdot \frac{1.0}{\sqrt{a - \frac{1.0}{3.0}}}\right) \cdot rand\right)\right)}\]

  9. Simplified0.2

    \[\leadsto 1 \cdot \color{blue}{\left(\left(a - \frac{1.0}{3.0}\right) \cdot \left(1.0 + \frac{rand \cdot \frac{1.0}{\sqrt{9.0}}}{\sqrt{a - \frac{1.0}{3.0}}}\right)\right)}\]

  10. Final simplification0.2

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(\frac{\frac{1.0}{\sqrt{9.0}} \cdot rand}{\sqrt{a - \frac{1.0}{3.0}}} + 1.0\right)\]

Reproduce

herbie shell --seed 2019165 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))))