Expression, p6

Average Error: 3.7 → 2.8

Time: 3.3s

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 r81707 = a;
        double r81708 = b;
        double r81709 = c;
        double r81710 = d;
        double r81711 = r81709 + r81710;
        double r81712 = r81708 + r81711;
        double r81713 = r81707 + r81712;
        double r81714 = 2.0;
        double r81715 = r81713 * r81714;
        return r81715;
}

↓

double f(double a, double b, double c, double d) {
        double r81716 = a;
        double r81717 = b;
        double r81718 = c;
        double r81719 = r81717 + r81718;
        double r81720 = d;
        double r81721 = r81719 + r81720;
        double r81722 = r81716 + r81721;
        double r81723 = 2.0;
        double r81724 = r81722 * r81723;
        return r81724;
}

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 2020060 
(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))