Expression, p6

Average Error: 3.7 → 2.8

Time: 13.0s

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 r80697 = a;
        double r80698 = b;
        double r80699 = c;
        double r80700 = d;
        double r80701 = r80699 + r80700;
        double r80702 = r80698 + r80701;
        double r80703 = r80697 + r80702;
        double r80704 = 2.0;
        double r80705 = r80703 * r80704;
        return r80705;
}

↓

double f(double a, double b, double c, double d) {
        double r80706 = a;
        double r80707 = b;
        double r80708 = c;
        double r80709 = r80707 + r80708;
        double r80710 = d;
        double r80711 = r80709 + r80710;
        double r80712 = r80706 + r80711;
        double r80713 = 2.0;
        double r80714 = r80712 * r80713;
        return r80714;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original	3.7
Target	3.9
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 2019322 +o rules:numerics
(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))