Average Error: 0.1 → 0.1
Time: 13.8s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \frac{\left(a - \frac{1}{3}\right) \cdot 1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\]
\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 + \frac{\left(a - \frac{1}{3}\right) \cdot 1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand
double f(double a, double rand) {
        double r147624 = a;
        double r147625 = 1.0;
        double r147626 = 3.0;
        double r147627 = r147625 / r147626;
        double r147628 = r147624 - r147627;
        double r147629 = 9.0;
        double r147630 = r147629 * r147628;
        double r147631 = sqrt(r147630);
        double r147632 = r147625 / r147631;
        double r147633 = rand;
        double r147634 = r147632 * r147633;
        double r147635 = r147625 + r147634;
        double r147636 = r147628 * r147635;
        return r147636;
}
↓
double f(double a, double rand) {
        double r147637 = a;
        double r147638 = 1.0;
        double r147639 = 3.0;
        double r147640 = r147638 / r147639;
        double r147641 = r147637 - r147640;
        double r147642 = r147641 * r147638;
        double r147643 = 9.0;
        double r147644 = r147643 * r147641;
        double r147645 = sqrt(r147644);
        double r147646 = r147642 / r147645;
        double r147647 = rand;
        double r147648 = r147646 * r147647;
        double r147649 = r147642 + r147648;
        return r147649;
}

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. Using strategy rm

  7. Applied associate-*r/0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))