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

Error

Bits error versus a

Bits error versus rand

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 0.1 bits

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

  2. SimplifiedError: 0.1 bits

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

  3. Final simplificationError: 0.1 bits

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

Reproduce

herbie shell --seed 2020204 
(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))))