Average Error: 0.1 → 0.1
Time: 8.7s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(\left(a - \frac{1}{3}\right) \cdot \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot rand\]
\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(\left(a - \frac{1}{3}\right) \cdot \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot rand
double f(double a, double rand) {
        double r92568 = a;
        double r92569 = 1.0;
        double r92570 = 3.0;
        double r92571 = r92569 / r92570;
        double r92572 = r92568 - r92571;
        double r92573 = 9.0;
        double r92574 = r92573 * r92572;
        double r92575 = sqrt(r92574);
        double r92576 = r92569 / r92575;
        double r92577 = rand;
        double r92578 = r92576 * r92577;
        double r92579 = r92569 + r92578;
        double r92580 = r92572 * r92579;
        return r92580;
}
↓
double f(double a, double rand) {
        double r92581 = a;
        double r92582 = 1.0;
        double r92583 = 3.0;
        double r92584 = r92582 / r92583;
        double r92585 = r92581 - r92584;
        double r92586 = r92585 * r92582;
        double r92587 = 9.0;
        double r92588 = r92587 * r92585;
        double r92589 = sqrt(r92588);
        double r92590 = r92582 / r92589;
        double r92591 = r92585 * r92590;
        double r92592 = rand;
        double r92593 = r92591 * r92592;
        double r92594 = r92586 + r92593;
        return r92594;
}

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 distribute-lft-in0.1

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

  5. Applied associate-*r*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020035 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))