Average Error: 0.1 → 0.2
Time: 32.4s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{9}} \cdot \left(\frac{\sqrt[3]{1}}{\sqrt{a - \frac{1}{3}}} \cdot rand\right)\right)\]
\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{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{9}} \cdot \left(\frac{\sqrt[3]{1}}{\sqrt{a - \frac{1}{3}}} \cdot rand\right)\right)
double f(double a, double rand) {
        double r81484 = a;
        double r81485 = 1.0;
        double r81486 = 3.0;
        double r81487 = r81485 / r81486;
        double r81488 = r81484 - r81487;
        double r81489 = 9.0;
        double r81490 = r81489 * r81488;
        double r81491 = sqrt(r81490);
        double r81492 = r81485 / r81491;
        double r81493 = rand;
        double r81494 = r81492 * r81493;
        double r81495 = r81485 + r81494;
        double r81496 = r81488 * r81495;
        return r81496;
}
↓
double f(double a, double rand) {
        double r81497 = a;
        double r81498 = 1.0;
        double r81499 = 3.0;
        double r81500 = r81498 / r81499;
        double r81501 = r81497 - r81500;
        double r81502 = cbrt(r81498);
        double r81503 = r81502 * r81502;
        double r81504 = 9.0;
        double r81505 = sqrt(r81504);
        double r81506 = r81503 / r81505;
        double r81507 = sqrt(r81501);
        double r81508 = r81502 / r81507;
        double r81509 = rand;
        double r81510 = r81508 * r81509;
        double r81511 = r81506 * r81510;
        double r81512 = r81498 + r81511;
        double r81513 = r81501 * r81512;
        return r81513;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019199 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))))