Average Error: 0.1 → 0.1
Time: 8.2s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{\left(\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}\right) \cdot \left(\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}\right)}}\right)\]
\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{\left(\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}\right) \cdot \left(\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}\right)}}\right)
double f(double a, double rand) {
        double r85497 = a;
        double r85498 = 1.0;
        double r85499 = 3.0;
        double r85500 = r85498 / r85499;
        double r85501 = r85497 - r85500;
        double r85502 = 9.0;
        double r85503 = r85502 * r85501;
        double r85504 = sqrt(r85503);
        double r85505 = r85498 / r85504;
        double r85506 = rand;
        double r85507 = r85505 * r85506;
        double r85508 = r85498 + r85507;
        double r85509 = r85501 * r85508;
        return r85509;
}
↓
double f(double a, double rand) {
        double r85510 = a;
        double r85511 = 1.0;
        double r85512 = 3.0;
        double r85513 = r85511 / r85512;
        double r85514 = r85510 - r85513;
        double r85515 = rand;
        double r85516 = r85511 * r85515;
        double r85517 = 9.0;
        double r85518 = sqrt(r85517);
        double r85519 = sqrt(r85514);
        double r85520 = r85518 * r85519;
        double r85521 = r85520 * r85520;
        double r85522 = sqrt(r85521);
        double r85523 = r85516 / r85522;
        double r85524 = r85511 + r85523;
        double r85525 = r85514 * r85524;
        return r85525;
}

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 add-sqr-sqrt0.1

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

  6. Applied add-sqr-sqrt0.1

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

  7. Applied unswap-sqr0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020018 +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))))