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 r113307 = a;
        double r113308 = b;
        double r113309 = c;
        double r113310 = d;
        double r113311 = r113309 + r113310;
        double r113312 = r113308 + r113311;
        double r113313 = r113307 + r113312;
        double r113314 = 2.0;
        double r113315 = r113313 * r113314;
        return r113315;
}

↓

double f(double a, double b, double c, double d) {
        double r113316 = a;
        double r113317 = b;
        double r113318 = c;
        double r113319 = r113317 + r113318;
        double r113320 = d;
        double r113321 = r113319 + r113320;
        double r113322 = r113316 + r113321;
        double r113323 = 2.0;
        double r113324 = r113322 * r113323;
        return r113324;
}

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))