Expression, p6

Average Error: 3.7 → 2.8

Time: 3.3s

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 r89793 = a;
        double r89794 = b;
        double r89795 = c;
        double r89796 = d;
        double r89797 = r89795 + r89796;
        double r89798 = r89794 + r89797;
        double r89799 = r89793 + r89798;
        double r89800 = 2.0;
        double r89801 = r89799 * r89800;
        return r89801;
}

↓

double f(double a, double b, double c, double d) {
        double r89802 = a;
        double r89803 = b;
        double r89804 = c;
        double r89805 = r89803 + r89804;
        double r89806 = d;
        double r89807 = r89805 + r89806;
        double r89808 = r89802 + r89807;
        double r89809 = 2.0;
        double r89810 = r89808 * r89809;
        return r89810;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original	3.7
Target	3.8
Herbie	2.8

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

Derivation

1. Initial program 3.7

   \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
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 2020018 
(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))