Expression, p6

Average Error: 3.7 → 2.8

Time: 3.8s

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 r103860 = a;
        double r103861 = b;
        double r103862 = c;
        double r103863 = d;
        double r103864 = r103862 + r103863;
        double r103865 = r103861 + r103864;
        double r103866 = r103860 + r103865;
        double r103867 = 2.0;
        double r103868 = r103866 * r103867;
        return r103868;
}

↓

double f(double a, double b, double c, double d) {
        double r103869 = a;
        double r103870 = b;
        double r103871 = c;
        double r103872 = r103870 + r103871;
        double r103873 = d;
        double r103874 = r103872 + r103873;
        double r103875 = r103869 + r103874;
        double r103876 = 2.0;
        double r103877 = r103875 * r103876;
        return r103877;
}

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 2020001 
(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))