Expression, p6

Average Error: 3.7 → 2.8

Time: 2.8s

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 r103754 = a;
        double r103755 = b;
        double r103756 = c;
        double r103757 = d;
        double r103758 = r103756 + r103757;
        double r103759 = r103755 + r103758;
        double r103760 = r103754 + r103759;
        double r103761 = 2.0;
        double r103762 = r103760 * r103761;
        return r103762;
}

↓

double f(double a, double b, double c, double d) {
        double r103763 = a;
        double r103764 = b;
        double r103765 = c;
        double r103766 = r103764 + r103765;
        double r103767 = d;
        double r103768 = r103766 + r103767;
        double r103769 = r103763 + r103768;
        double r103770 = 2.0;
        double r103771 = r103769 * r103770;
        return r103771;
}

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 2020059 
(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))