Average Error: 0.1 → 0.1
Time: 7.0s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{\frac{1 \cdot rand}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}}\right)\]
\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{\frac{1 \cdot rand}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}}\right)
double f(double a, double rand) {
        double r69535 = a;
        double r69536 = 1.0;
        double r69537 = 3.0;
        double r69538 = r69536 / r69537;
        double r69539 = r69535 - r69538;
        double r69540 = 9.0;
        double r69541 = r69540 * r69539;
        double r69542 = sqrt(r69541);
        double r69543 = r69536 / r69542;
        double r69544 = rand;
        double r69545 = r69543 * r69544;
        double r69546 = r69536 + r69545;
        double r69547 = r69539 * r69546;
        return r69547;
}
↓
double f(double a, double rand) {
        double r69548 = a;
        double r69549 = 1.0;
        double r69550 = 3.0;
        double r69551 = r69549 / r69550;
        double r69552 = r69548 - r69551;
        double r69553 = rand;
        double r69554 = r69549 * r69553;
        double r69555 = 9.0;
        double r69556 = sqrt(r69555);
        double r69557 = r69554 / r69556;
        double r69558 = sqrt(r69552);
        double r69559 = r69557 / r69558;
        double r69560 = r69549 + r69559;
        double r69561 = r69552 * r69560;
        return r69561;
}

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 associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019352 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))