Average Error: 0.1 → 0.1
Time: 29.1s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \left(\frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
\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 + \left(a - \frac{1}{3}\right) \cdot \left(\frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
double f(double a, double rand) {
        double r92411 = a;
        double r92412 = 1.0;
        double r92413 = 3.0;
        double r92414 = r92412 / r92413;
        double r92415 = r92411 - r92414;
        double r92416 = 9.0;
        double r92417 = r92416 * r92415;
        double r92418 = sqrt(r92417);
        double r92419 = r92412 / r92418;
        double r92420 = rand;
        double r92421 = r92419 * r92420;
        double r92422 = r92412 + r92421;
        double r92423 = r92415 * r92422;
        return r92423;
}
↓
double f(double a, double rand) {
        double r92424 = a;
        double r92425 = 1.0;
        double r92426 = 3.0;
        double r92427 = r92425 / r92426;
        double r92428 = r92424 - r92427;
        double r92429 = r92428 * r92425;
        double r92430 = 9.0;
        double r92431 = r92430 * r92428;
        double r92432 = sqrt(r92431);
        double r92433 = r92425 / r92432;
        double r92434 = rand;
        double r92435 = r92433 * r92434;
        double r92436 = r92428 * r92435;
        double r92437 = r92429 + r92436;
        return r92437;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))