Expression, p6

Average Error: 3.7 → 2.7

Time: 8.3s

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 r60102 = a;
        double r60103 = b;
        double r60104 = c;
        double r60105 = d;
        double r60106 = r60104 + r60105;
        double r60107 = r60103 + r60106;
        double r60108 = r60102 + r60107;
        double r60109 = 2.0;
        double r60110 = r60108 * r60109;
        return r60110;
}

↓

double f(double a, double b, double c, double d) {
        double r60111 = a;
        double r60112 = b;
        double r60113 = c;
        double r60114 = r60112 + r60113;
        double r60115 = d;
        double r60116 = r60114 + r60115;
        double r60117 = r60111 + r60116;
        double r60118 = 2.0;
        double r60119 = r60117 * r60118;
        return r60119;
}

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	2.7

\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

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+ 2.7

   \[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]

4. Final simplification 2.7

   \[\leadsto \left(a + \left(\left(b + c\right) + d\right)\right) \cdot 2\]

Reproduce

herbie shell --seed 2019297 
(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))