Average Error: 0.1 → 0.1
Time: 5.2s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \frac{a - \frac{1}{3}}{\frac{\frac{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}{1}}{rand}}\]
\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{a - \frac{1}{3}}{\frac{\frac{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}{1}}{rand}}
double code(double a, double rand) {
	return ((a - (1.0 / 3.0)) * (1.0 + ((1.0 / sqrt((9.0 * (a - (1.0 / 3.0))))) * rand)));
}
↓
double code(double a, double rand) {
	return (((a - (1.0 / 3.0)) * 1.0) + ((a - (1.0 / 3.0)) / ((sqrt((9.0 * (a - (1.0 / 3.0)))) / 1.0) / 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 clear-num0.1

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

  4. Applied associate-*l/0.1

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

  5. Simplified0.1

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

  7. Applied clear-num0.1

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

  9. Applied distribute-lft-in0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020071 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))