Expression, p6

Average Error: 3.6 → 2.8

Time: 3.2s

Precision: 64

\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]

Math

\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]

↓

\[\left(a + \left(\left(b + c\right) + d\right)\right) \cdot 2\]

C

double f(double a, double b, double c, double d) {
        double r102825 = a;
        double r102826 = b;
        double r102827 = c;
        double r102828 = d;
        double r102829 = r102827 + r102828;
        double r102830 = r102826 + r102829;
        double r102831 = r102825 + r102830;
        double r102832 = 2.0;
        double r102833 = r102831 * r102832;
        return r102833;
}

↓

double f(double a, double b, double c, double d) {
        double r102834 = a;
        double r102835 = b;
        double r102836 = c;
        double r102837 = r102835 + r102836;
        double r102838 = d;
        double r102839 = r102837 + r102838;
        double r102840 = r102834 + r102839;
        double r102841 = 2.0;
        double r102842 = r102840 * r102841;
        return r102842;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original	3.6
Target	3.8
Herbie	2.8

\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

1. Initial program 3.6

   \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
2. Using strategy rm

3. Applied associate-+r+ 2.8

   \[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]

4. Final simplification 2.8

   \[\leadsto \left(a + \left(\left(b + c\right) + d\right)\right) \cdot 2\]

Reproduce

herbie shell --seed 2020034 
(FPCore (a b c d)
  :name "Expression, p6"
  :precision binary64
  :pre (and (<= -14 a -13) (<= -3 b -2) (<= 3 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2) (* (+ c d) 2))

  (* (+ a (+ b (+ c d))) 2))