Average Error: 0.1 → 0.1
Time: 7.1s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{\frac{1 \cdot rand}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}}\right)\]
\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 \left(1 + \frac{\frac{1 \cdot rand}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}}\right)
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 + (((1.0 * rand) / sqrt(9.0)) / sqrt((a - (1.0 / 3.0))))));
}

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. Using strategy rm

  5. Applied sqrt-prod0.1

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020057 +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))))