Average Error: 0.1 → 0.2
Time: 7.1s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9}} \cdot \frac{rand}{\sqrt{a - \frac{1}{3}}}\right)\]
\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 + \frac{1}{\sqrt{9}} \cdot \frac{rand}{\sqrt{a - \frac{1}{3}}}\right)
double f(double a, double rand) {
        double r67523 = a;
        double r67524 = 1.0;
        double r67525 = 3.0;
        double r67526 = r67524 / r67525;
        double r67527 = r67523 - r67526;
        double r67528 = 9.0;
        double r67529 = r67528 * r67527;
        double r67530 = sqrt(r67529);
        double r67531 = r67524 / r67530;
        double r67532 = rand;
        double r67533 = r67531 * r67532;
        double r67534 = r67524 + r67533;
        double r67535 = r67527 * r67534;
        return r67535;
}
↓
double f(double a, double rand) {
        double r67536 = a;
        double r67537 = 1.0;
        double r67538 = 3.0;
        double r67539 = r67537 / r67538;
        double r67540 = r67536 - r67539;
        double r67541 = 9.0;
        double r67542 = sqrt(r67541);
        double r67543 = r67537 / r67542;
        double r67544 = rand;
        double r67545 = sqrt(r67540);
        double r67546 = r67544 / r67545;
        double r67547 = r67543 * r67546;
        double r67548 = r67537 + r67547;
        double r67549 = r67540 * r67548;
        return r67549;
}

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 associate-*l/0.1

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

  5. Applied sqrt-prod0.1

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

  6. Applied times-frac0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020064 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))