Expression, p6

Average Error: 3.7 → 2.8

Time: 2.9s

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 r90494 = a;
        double r90495 = b;
        double r90496 = c;
        double r90497 = d;
        double r90498 = r90496 + r90497;
        double r90499 = r90495 + r90498;
        double r90500 = r90494 + r90499;
        double r90501 = 2.0;
        double r90502 = r90500 * r90501;
        return r90502;
}

↓

double f(double a, double b, double c, double d) {
        double r90503 = a;
        double r90504 = b;
        double r90505 = c;
        double r90506 = r90504 + r90505;
        double r90507 = d;
        double r90508 = r90506 + r90507;
        double r90509 = r90503 + r90508;
        double r90510 = 2.0;
        double r90511 = r90509 * r90510;
        return r90511;
}

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 2020062 
(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))