Octave 3.8, oct_fill_randg

Average Error: 0.1 → 0.1

Time: 12.1s

Precision: binary64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

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(((double) (9.0 * ((double) (a - (1.0 / 3.0))))))))))))));
}

Error

Bits error versus a

Bits error versus rand

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 0.1

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

4. Applied associate-*l* 0.1

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

5. Simplified 0.1

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

6. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020182 
(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))))