Average Error: 0.1 → 0.1
Time: 4.1s
Precision: binary64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[1 \cdot \left(\left(a - \frac{1}{3}\right) \cdot \left(\frac{\frac{rand}{\sqrt{a - \frac{1}{3}}}}{\sqrt{9}} + 1\right)\right)\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
1 \cdot \left(\left(a - \frac{1}{3}\right) \cdot \left(\frac{\frac{rand}{\sqrt{a - \frac{1}{3}}}}{\sqrt{9}} + 1\right)\right)
double code(double a, double rand) {
	return ((double) (((double) (a - (1.0 / 3.0))) * ((double) (1.0 + ((double) ((1.0 / ((double) sqrt(((double) (9.0 * ((double) (a - (1.0 / 3.0)))))))) * rand))))));
}
↓
double code(double a, double rand) {
	return ((double) (1.0 * ((double) (((double) (a - (1.0 / 3.0))) * ((double) (((rand / ((double) sqrt(((double) (a - (1.0 / 3.0)))))) / ((double) sqrt(9.0))) + 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. Simplified0.1

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

  4. Applied sqrt-prod0.1

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

  5. Applied associate-/r*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020196 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))))