Average Error: 0.1 → 0.1
Time: 7.6s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\]
\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 \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}
double f(double a, double rand) {
        double r56622 = a;
        double r56623 = 1.0;
        double r56624 = 3.0;
        double r56625 = r56623 / r56624;
        double r56626 = r56622 - r56625;
        double r56627 = 9.0;
        double r56628 = r56627 * r56626;
        double r56629 = sqrt(r56628);
        double r56630 = r56623 / r56629;
        double r56631 = rand;
        double r56632 = r56630 * r56631;
        double r56633 = r56623 + r56632;
        double r56634 = r56626 * r56633;
        return r56634;
}
↓
double f(double a, double rand) {
        double r56635 = a;
        double r56636 = 1.0;
        double r56637 = 3.0;
        double r56638 = r56636 / r56637;
        double r56639 = r56635 - r56638;
        double r56640 = r56639 * r56636;
        double r56641 = rand;
        double r56642 = r56636 * r56641;
        double r56643 = 9.0;
        double r56644 = r56643 * r56639;
        double r56645 = sqrt(r56644);
        double r56646 = r56642 / r56645;
        double r56647 = r56639 * r56646;
        double r56648 = r56640 + r56647;
        return r56648;
}

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 distribute-lft-in0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019344 +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))))