Average Error: 0.1 → 0.1
Time: 30.6s
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 r138462 = a;
        double r138463 = 1.0;
        double r138464 = 3.0;
        double r138465 = r138463 / r138464;
        double r138466 = r138462 - r138465;
        double r138467 = 9.0;
        double r138468 = r138467 * r138466;
        double r138469 = sqrt(r138468);
        double r138470 = r138463 / r138469;
        double r138471 = rand;
        double r138472 = r138470 * r138471;
        double r138473 = r138463 + r138472;
        double r138474 = r138466 * r138473;
        return r138474;
}
↓
double f(double a, double rand) {
        double r138475 = a;
        double r138476 = 1.0;
        double r138477 = 3.0;
        double r138478 = r138476 / r138477;
        double r138479 = r138475 - r138478;
        double r138480 = 1.0;
        double r138481 = 9.0;
        double r138482 = r138481 * r138479;
        double r138483 = sqrt(r138482);
        double r138484 = rand;
        double r138485 = r138483 / r138484;
        double r138486 = r138480 / r138485;
        double r138487 = r138476 * r138486;
        double r138488 = r138476 + r138487;
        double r138489 = r138479 * r138488;
        return r138489;
}

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))))