Expression, p6

Average Error: 3.6 → 2.8

Time: 10.2s

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 r60744 = a;
        double r60745 = b;
        double r60746 = c;
        double r60747 = d;
        double r60748 = r60746 + r60747;
        double r60749 = r60745 + r60748;
        double r60750 = r60744 + r60749;
        double r60751 = 2.0;
        double r60752 = r60750 * r60751;
        return r60752;
}

↓

double f(double a, double b, double c, double d) {
        double r60753 = a;
        double r60754 = b;
        double r60755 = c;
        double r60756 = r60754 + r60755;
        double r60757 = d;
        double r60758 = r60756 + r60757;
        double r60759 = r60753 + r60758;
        double r60760 = 2.0;
        double r60761 = r60759 * r60760;
        return r60761;
}

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 2019325 
(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))