Expression, p6

Average Error: 3.7 → 2.8

Time: 3.7s

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 r110117 = a;
        double r110118 = b;
        double r110119 = c;
        double r110120 = d;
        double r110121 = r110119 + r110120;
        double r110122 = r110118 + r110121;
        double r110123 = r110117 + r110122;
        double r110124 = 2.0;
        double r110125 = r110123 * r110124;
        return r110125;
}

↓

double f(double a, double b, double c, double d) {
        double r110126 = a;
        double r110127 = b;
        double r110128 = c;
        double r110129 = r110127 + r110128;
        double r110130 = d;
        double r110131 = r110129 + r110130;
        double r110132 = r110126 + r110131;
        double r110133 = 2.0;
        double r110134 = r110132 * r110133;
        return r110134;
}

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 2020081 +o rules:numerics
(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))