Expression 1, p15

Average Error: 0.4 → 0.3

Time: 10.9s

Precision: 64

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

Math

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

↓

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

C

double f(double a, double b, double c, double d, double e) {
        double r4726681 = e;
        double r4726682 = d;
        double r4726683 = r4726681 + r4726682;
        double r4726684 = c;
        double r4726685 = r4726683 + r4726684;
        double r4726686 = b;
        double r4726687 = r4726685 + r4726686;
        double r4726688 = a;
        double r4726689 = r4726687 + r4726688;
        return r4726689;
}

↓

double f(double a, double b, double c, double d, double e) {
        double r4726690 = c;
        double r4726691 = b;
        double r4726692 = r4726690 + r4726691;
        double r4726693 = a;
        double r4726694 = r4726692 + r4726693;
        double r4726695 = d;
        double r4726696 = e;
        double r4726697 = r4726695 + r4726696;
        double r4726698 = r4726694 + r4726697;
        return r4726698;
}

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

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

5. Applied associate-+l+ 0.3

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

6. Final simplification 0.3

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

Reproduce

herbie shell --seed 2019164 
(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))