Expression, p6

Average Error: 3.6 → 2.8

Time: 2.6s

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 r104756 = a;
        double r104757 = b;
        double r104758 = c;
        double r104759 = d;
        double r104760 = r104758 + r104759;
        double r104761 = r104757 + r104760;
        double r104762 = r104756 + r104761;
        double r104763 = 2.0;
        double r104764 = r104762 * r104763;
        return r104764;
}

↓

double f(double a, double b, double c, double d) {
        double r104765 = a;
        double r104766 = b;
        double r104767 = c;
        double r104768 = r104766 + r104767;
        double r104769 = d;
        double r104770 = r104768 + r104769;
        double r104771 = r104765 + r104770;
        double r104772 = 2.0;
        double r104773 = r104771 * r104772;
        return r104773;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original	3.6
Target	3.9
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 2020056 
(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))