Average Error: 0.1 → 0.1
Time: 6.8s
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 code(double a, double rand) {
	return ((double) (((double) (a - ((double) (1.0 / 3.0)))) * ((double) (1.0 + ((double) (((double) (1.0 / ((double) sqrt(((double) (9.0 * ((double) (a - ((double) (1.0 / 3.0)))))))))) * rand))))));
}
↓
double code(double a, double rand) {
	return ((double) (((double) (((double) (a - ((double) (1.0 / 3.0)))) * 1.0)) + ((double) (((double) (((double) (((double) (a - ((double) (1.0 / 3.0)))) * 1.0)) / ((double) sqrt(((double) (9.0 * ((double) (a - ((double) (1.0 / 3.0)))))))))) * rand))));
}

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 2020121 +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))))