Average Error: 0.1 → 0.1
Time: 27.9s
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 r85458 = a;
        double r85459 = 1.0;
        double r85460 = 3.0;
        double r85461 = r85459 / r85460;
        double r85462 = r85458 - r85461;
        double r85463 = 9.0;
        double r85464 = r85463 * r85462;
        double r85465 = sqrt(r85464);
        double r85466 = r85459 / r85465;
        double r85467 = rand;
        double r85468 = r85466 * r85467;
        double r85469 = r85459 + r85468;
        double r85470 = r85462 * r85469;
        return r85470;
}
↓
double f(double a, double rand) {
        double r85471 = a;
        double r85472 = 1.0;
        double r85473 = 3.0;
        double r85474 = r85472 / r85473;
        double r85475 = r85471 - r85474;
        double r85476 = 1.0;
        double r85477 = 9.0;
        double r85478 = r85477 * r85475;
        double r85479 = sqrt(r85478);
        double r85480 = rand;
        double r85481 = r85479 / r85480;
        double r85482 = r85476 / r85481;
        double r85483 = r85472 * r85482;
        double r85484 = r85472 + r85483;
        double r85485 = r85475 * r85484;
        return r85485;
}

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 +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))))