Expression, p6

Average Error: 3.7 → 2.8

Time: 2.7s

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 r75437 = a;
        double r75438 = b;
        double r75439 = c;
        double r75440 = d;
        double r75441 = r75439 + r75440;
        double r75442 = r75438 + r75441;
        double r75443 = r75437 + r75442;
        double r75444 = 2.0;
        double r75445 = r75443 * r75444;
        return r75445;
}

↓

double f(double a, double b, double c, double d) {
        double r75446 = a;
        double r75447 = b;
        double r75448 = c;
        double r75449 = r75447 + r75448;
        double r75450 = d;
        double r75451 = r75449 + r75450;
        double r75452 = r75446 + r75451;
        double r75453 = 2.0;
        double r75454 = r75452 * r75453;
        return r75454;
}

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 2020100 
(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))