Expression, p6

Average Error: 3.7 → 2.8

Time: 48.9s

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

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

↓

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

C

double f(double a, double b, double c, double d) {
        double r40886705 = a;
        double r40886706 = b;
        double r40886707 = c;
        double r40886708 = d;
        double r40886709 = r40886707 + r40886708;
        double r40886710 = r40886706 + r40886709;
        double r40886711 = r40886705 + r40886710;
        double r40886712 = 2.0;
        double r40886713 = r40886711 * r40886712;
        return r40886713;
}

↓

double f(double a, double b, double c, double d) {
        double r40886714 = 2.0;
        double r40886715 = b;
        double r40886716 = c;
        double r40886717 = r40886715 + r40886716;
        double r40886718 = d;
        double r40886719 = r40886717 + r40886718;
        double r40886720 = a;
        double r40886721 = r40886719 + r40886720;
        double r40886722 = r40886714 * r40886721;
        return r40886722;
}

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

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

Reproduce

herbie shell --seed 2019120 
(FPCore (a b c d)
  :name "Expression, p6"
  :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))