Average Error: 0.1 → 0.1
Time: 16.2s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{9}} \cdot \frac{\sqrt[3]{1} \cdot rand}{\sqrt{a - \frac{1}{3}}}\right)\]
\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 1 + \left(a - \frac{1}{3}\right) \cdot \left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{9}} \cdot \frac{\sqrt[3]{1} \cdot rand}{\sqrt{a - \frac{1}{3}}}\right)
double f(double a, double rand) {
        double r389 = a;
        double r390 = 1.0;
        double r391 = 3.0;
        double r392 = r390 / r391;
        double r393 = r389 - r392;
        double r394 = 9.0;
        double r395 = r394 * r393;
        double r396 = sqrt(r395);
        double r397 = r390 / r396;
        double r398 = rand;
        double r399 = r397 * r398;
        double r400 = r390 + r399;
        double r401 = r393 * r400;
        return r401;
}
↓
double f(double a, double rand) {
        double r402 = a;
        double r403 = 1.0;
        double r404 = 3.0;
        double r405 = r403 / r404;
        double r406 = r402 - r405;
        double r407 = r406 * r403;
        double r408 = cbrt(r403);
        double r409 = r408 * r408;
        double r410 = 9.0;
        double r411 = sqrt(r410);
        double r412 = r409 / r411;
        double r413 = rand;
        double r414 = r408 * r413;
        double r415 = sqrt(r406);
        double r416 = r414 / r415;
        double r417 = r412 * r416;
        double r418 = r406 * r417;
        double r419 = r407 + r418;
        return r419;
}

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-cube-cbrt0.2

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

  5. Applied times-frac0.2

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

  6. Applied associate-*l*0.2

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

  8. Applied distribute-lft-in0.2

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

  10. Applied associate-*l/0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020025 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))