Expression 1, p15

Average Error: 0.4 → 0.3

Time: 9.7s

Precision: 64

\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]

Math

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

↓

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

C

double f(double a, double b, double c, double d, double e) {
        double r5244902 = e;
        double r5244903 = d;
        double r5244904 = r5244902 + r5244903;
        double r5244905 = c;
        double r5244906 = r5244904 + r5244905;
        double r5244907 = b;
        double r5244908 = r5244906 + r5244907;
        double r5244909 = a;
        double r5244910 = r5244908 + r5244909;
        return r5244910;
}

↓

double f(double a, double b, double c, double d, double e) {
        double r5244911 = b;
        double r5244912 = a;
        double r5244913 = r5244911 + r5244912;
        double r5244914 = d;
        double r5244915 = c;
        double r5244916 = r5244914 + r5244915;
        double r5244917 = e;
        double r5244918 = r5244916 + r5244917;
        double r5244919 = r5244913 + r5244918;
        return r5244919;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Target

Original	0.4
Target	0.2
Herbie	0.3

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

Derivation

1. Initial program 0.4

   \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
2. Using strategy rm

3. Applied associate-+l+ 0.3

   \[\leadsto \color{blue}{\left(\left(e + d\right) + c\right) + \left(b + a\right)}\]
4. Using strategy rm

5. Applied associate-+l+ 0.3

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

6. Final simplification 0.3

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

Reproduce

herbie shell --seed 2019165 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))