Average Error: 0.1 → 0.1
Time: 17.3s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}}\right)\]
\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 \cdot rand}{\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}}\right)
double f(double a, double rand) {
        double r109438 = a;
        double r109439 = 1.0;
        double r109440 = 3.0;
        double r109441 = r109439 / r109440;
        double r109442 = r109438 - r109441;
        double r109443 = 9.0;
        double r109444 = r109443 * r109442;
        double r109445 = sqrt(r109444);
        double r109446 = r109439 / r109445;
        double r109447 = rand;
        double r109448 = r109446 * r109447;
        double r109449 = r109439 + r109448;
        double r109450 = r109442 * r109449;
        return r109450;
}
↓
double f(double a, double rand) {
        double r109451 = a;
        double r109452 = 1.0;
        double r109453 = 3.0;
        double r109454 = r109452 / r109453;
        double r109455 = r109451 - r109454;
        double r109456 = rand;
        double r109457 = r109452 * r109456;
        double r109458 = 9.0;
        double r109459 = sqrt(r109458);
        double r109460 = sqrt(r109455);
        double r109461 = r109459 * r109460;
        double r109462 = r109457 / r109461;
        double r109463 = r109452 + r109462;
        double r109464 = r109455 * r109463;
        return r109464;
}

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 sqrt-prod0.2

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

  4. Applied add-sqr-sqrt0.2

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

  5. Applied times-frac0.2

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

  6. Applied associate-*l*0.2

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

  8. Applied associate-*l/0.2

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

  9. Applied frac-times0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))