Average Error: 0.1 → 0.1
Time: 11.5s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right)\]
\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{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right)
double f(double a, double rand) {
        double r91603 = a;
        double r91604 = 1.0;
        double r91605 = 3.0;
        double r91606 = r91604 / r91605;
        double r91607 = r91603 - r91606;
        double r91608 = 9.0;
        double r91609 = r91608 * r91607;
        double r91610 = sqrt(r91609);
        double r91611 = r91604 / r91610;
        double r91612 = rand;
        double r91613 = r91611 * r91612;
        double r91614 = r91604 + r91613;
        double r91615 = r91607 * r91614;
        return r91615;
}
↓
double f(double a, double rand) {
        double r91616 = a;
        double r91617 = 1.0;
        double r91618 = 3.0;
        double r91619 = r91617 / r91618;
        double r91620 = r91616 - r91619;
        double r91621 = rand;
        double r91622 = r91617 * r91621;
        double r91623 = 9.0;
        double r91624 = r91623 * r91620;
        double r91625 = sqrt(r91624);
        double r91626 = r91622 / r91625;
        double r91627 = r91617 + r91626;
        double r91628 = r91620 * r91627;
        return r91628;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))