Average Error: 0.1 → 0.1
Time: 12.4s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\frac{1 \cdot \left(a - \frac{1}{3}\right)}{\frac{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}{rand}} + \left(a - \frac{1}{3}\right) \cdot 1\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\frac{1 \cdot \left(a - \frac{1}{3}\right)}{\frac{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}{rand}} + \left(a - \frac{1}{3}\right) \cdot 1
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 (((1.0 * (a - (1.0 / 3.0))) / (sqrt((9.0 * (a - (1.0 / 3.0)))) / rand)) + ((a - (1.0 / 3.0)) * 1.0));
}

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. Simplified0.1

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

  6. Applied +-commutative0.1

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

  7. Applied distribute-lft-in0.1

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

  9. Applied *-commutative0.1

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

  10. Applied associate-/l*0.1

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

  11. Applied associate-*r/0.1

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2020066 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))