Octave 3.8, oct_fill_randg

Average Error: 0.1 → 0.1

Time: 25.3s

Precision: 64

Math

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

↓

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

C

double code(double a, double rand) {
	return ((double) (((double) (a - ((double) (1.0 / 3.0)))) * ((double) (1.0 + ((double) (((double) (1.0 / ((double) sqrt(((double) (9.0 * ((double) (a - ((double) (1.0 / 3.0)))))))))) * rand))))));
}

↓

double code(double a, double rand) {
	return ((double) (((double) (a - ((double) (1.0 / 3.0)))) * ((double) (1.0 + ((double) (((double) (((double) -(1.0)) * rand)) / ((double) -(((double) sqrt(((double) (9.0 * ((double) (a - ((double) (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 frac-2neg 0.1

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

4. Applied associate-*l/ 0.1

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

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020114 +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))))