Average Error: 0.1 → 0.1
Time: 31.7s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + 1 \cdot \frac{1}{\frac{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}{rand}}\right)\]
\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 \left(1 + 1 \cdot \frac{1}{\frac{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}{rand}}\right)
double f(double a, double rand) {
        double r135407 = a;
        double r135408 = 1.0;
        double r135409 = 3.0;
        double r135410 = r135408 / r135409;
        double r135411 = r135407 - r135410;
        double r135412 = 9.0;
        double r135413 = r135412 * r135411;
        double r135414 = sqrt(r135413);
        double r135415 = r135408 / r135414;
        double r135416 = rand;
        double r135417 = r135415 * r135416;
        double r135418 = r135408 + r135417;
        double r135419 = r135411 * r135418;
        return r135419;
}
↓
double f(double a, double rand) {
        double r135420 = a;
        double r135421 = 1.0;
        double r135422 = 3.0;
        double r135423 = r135421 / r135422;
        double r135424 = r135420 - r135423;
        double r135425 = 1.0;
        double r135426 = 9.0;
        double r135427 = r135426 * r135424;
        double r135428 = sqrt(r135427);
        double r135429 = rand;
        double r135430 = r135428 / r135429;
        double r135431 = r135425 / r135430;
        double r135432 = r135421 * r135431;
        double r135433 = r135421 + r135432;
        double r135434 = r135424 * r135433;
        return r135434;
}

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 div-inv0.1

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

  4. Applied associate-*l*0.1

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

  5. Simplified0.1

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

  7. Applied clear-num0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))