Average Error: 0.1 → 0.1
Time: 1.2m
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + {\left(9 \cdot \left(a - \frac{1.0}{3.0}\right)\right)}^{\frac{-1}{2}} \cdot rand\right)\]
\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)
↓
\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + {\left(9 \cdot \left(a - \frac{1.0}{3.0}\right)\right)}^{\frac{-1}{2}} \cdot rand\right)
double f(double a, double rand) {
        double r5193441 = a;
        double r5193442 = 1.0;
        double r5193443 = 3.0;
        double r5193444 = r5193442 / r5193443;
        double r5193445 = r5193441 - r5193444;
        double r5193446 = 1.0;
        double r5193447 = 9.0;
        double r5193448 = r5193447 * r5193445;
        double r5193449 = sqrt(r5193448);
        double r5193450 = r5193446 / r5193449;
        double r5193451 = rand;
        double r5193452 = r5193450 * r5193451;
        double r5193453 = r5193446 + r5193452;
        double r5193454 = r5193445 * r5193453;
        return r5193454;
}
↓
double f(double a, double rand) {
        double r5193455 = a;
        double r5193456 = 1.0;
        double r5193457 = 3.0;
        double r5193458 = r5193456 / r5193457;
        double r5193459 = r5193455 - r5193458;
        double r5193460 = 1.0;
        double r5193461 = 9.0;
        double r5193462 = r5193461 * r5193459;
        double r5193463 = -0.5;
        double r5193464 = pow(r5193462, r5193463);
        double r5193465 = rand;
        double r5193466 = r5193464 * r5193465;
        double r5193467 = r5193460 + r5193466;
        double r5193468 = r5193459 * r5193467;
        return r5193468;
}

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

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

  3. Applied pow1/20.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\color{blue}{{\left(9 \cdot \left(a - \frac{1.0}{3.0}\right)\right)}^{\frac{1}{2}}}} \cdot rand\right)\]

  4. Applied pow-flip0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \color{blue}{{\left(9 \cdot \left(a - \frac{1.0}{3.0}\right)\right)}^{\left(-\frac{1}{2}\right)}} \cdot rand\right)\]

  5. Simplified0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + {\left(9 \cdot \left(a - \frac{1.0}{3.0}\right)\right)}^{\color{blue}{\frac{-1}{2}}} \cdot rand\right)\]

  6. Final simplification0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + {\left(9 \cdot \left(a - \frac{1.0}{3.0}\right)\right)}^{\frac{-1}{2}} \cdot rand\right)\]

Reproduce

herbie shell --seed 2019124 
(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))))