Expression, p6

Average Error: 3.7 → 2.8

Time: 3.0s

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 r99852 = a;
        double r99853 = b;
        double r99854 = c;
        double r99855 = d;
        double r99856 = r99854 + r99855;
        double r99857 = r99853 + r99856;
        double r99858 = r99852 + r99857;
        double r99859 = 2.0;
        double r99860 = r99858 * r99859;
        return r99860;
}

↓

double f(double a, double b, double c, double d) {
        double r99861 = a;
        double r99862 = b;
        double r99863 = c;
        double r99864 = r99862 + r99863;
        double r99865 = d;
        double r99866 = r99864 + r99865;
        double r99867 = r99861 + r99866;
        double r99868 = 2.0;
        double r99869 = r99867 * r99868;
        return r99869;
}

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 2019362 
(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))