Average Error: 0.1 → 0.1
Time: 5.1s
Precision: binary64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + 1 \cdot \frac{\frac{rand}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}}\right)\]
\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 + 1 \cdot \frac{\frac{rand}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}}\right)
(FPCore (a rand)
 :precision binary64
 (*
  (- a (/ 1.0 3.0))
  (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))))
↓
(FPCore (a rand)
 :precision binary64
 (*
  (- a (/ 1.0 3.0))
  (+ 1.0 (* 1.0 (/ (/ rand (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))))
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) (((double) (a - (1.0 / 3.0))) * ((double) (1.0 + ((double) (1.0 * ((rand / ((double) sqrt(9.0))) / ((double) sqrt(((double) (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 div-inv_binary640.1

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

  4. Applied associate-*l*_binary640.1

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

  5. Simplified0.1

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

  7. Applied sqrt-prod_binary640.1

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

  8. Applied associate-/r*_binary640.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020210 
(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))))