Expression, p6

Average Error: 3.7 → 2.8

Time: 3.4s

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 r77096 = a;
        double r77097 = b;
        double r77098 = c;
        double r77099 = d;
        double r77100 = r77098 + r77099;
        double r77101 = r77097 + r77100;
        double r77102 = r77096 + r77101;
        double r77103 = 2.0;
        double r77104 = r77102 * r77103;
        return r77104;
}

↓

double f(double a, double b, double c, double d) {
        double r77105 = a;
        double r77106 = b;
        double r77107 = c;
        double r77108 = r77106 + r77107;
        double r77109 = d;
        double r77110 = r77108 + r77109;
        double r77111 = r77105 + r77110;
        double r77112 = 2.0;
        double r77113 = r77111 * r77112;
        return r77113;
}

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 2020083 
(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))