Expression, p14

Average Error: 0.0 → 0.0

Time: 2.1s

Precision: 64

\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]

Math

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

↓

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

C

double f(double a, double b, double c, double d) {
        double r92871 = a;
        double r92872 = b;
        double r92873 = c;
        double r92874 = r92872 + r92873;
        double r92875 = d;
        double r92876 = r92874 + r92875;
        double r92877 = r92871 * r92876;
        return r92877;
}

↓

double f(double a, double b, double c, double d) {
        double r92878 = a;
        double r92879 = b;
        double r92880 = r92878 * r92879;
        double r92881 = c;
        double r92882 = r92878 * r92881;
        double r92883 = r92880 + r92882;
        double r92884 = d;
        double r92885 = r92878 * r92884;
        double r92886 = r92883 + r92885;
        return r92886;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

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

3. Applied distribute-lft-in 0.0

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

5. Applied distribute-lft-in 0.0

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

6. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020002 
(FPCore (a b c d)
  :name "Expression, p14"
  :precision binary64
  :pre (and (<= 56789 a 98765) (<= 0.0 b 1) (<= 0.0 c 0.0016773) (<= 0.0 d 0.0016773))

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

  (* a (+ (+ b c) d)))