Expression, p6

Average Error: 3.6 → 2.8

Time: 11.4s

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 r14713 = a;
        double r14714 = b;
        double r14715 = c;
        double r14716 = d;
        double r14717 = r14715 + r14716;
        double r14718 = r14714 + r14717;
        double r14719 = r14713 + r14718;
        double r14720 = 2.0;
        double r14721 = r14719 * r14720;
        return r14721;
}

↓

double f(double a, double b, double c, double d) {
        double r14722 = a;
        double r14723 = b;
        double r14724 = c;
        double r14725 = r14723 + r14724;
        double r14726 = d;
        double r14727 = r14725 + r14726;
        double r14728 = r14722 + r14727;
        double r14729 = 2.0;
        double r14730 = r14728 * r14729;
        return r14730;
}

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 2019315 
(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))