Expression, p6

Average Error: 3.6 → 2.8

Time: 11.3s

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 r108781 = a;
        double r108782 = b;
        double r108783 = c;
        double r108784 = d;
        double r108785 = r108783 + r108784;
        double r108786 = r108782 + r108785;
        double r108787 = r108781 + r108786;
        double r108788 = 2.0;
        double r108789 = r108787 * r108788;
        return r108789;
}

↓

double f(double a, double b, double c, double d) {
        double r108790 = a;
        double r108791 = b;
        double r108792 = c;
        double r108793 = r108791 + r108792;
        double r108794 = d;
        double r108795 = r108793 + r108794;
        double r108796 = r108790 + r108795;
        double r108797 = 2.0;
        double r108798 = r108796 * r108797;
        return r108798;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original	3.6
Target	3.8
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 2019303 
(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))