Expression, p14

Average Error: 0.0 → 0.0

Time: 2.6s

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 r112812 = a;
        double r112813 = b;
        double r112814 = c;
        double r112815 = r112813 + r112814;
        double r112816 = d;
        double r112817 = r112815 + r112816;
        double r112818 = r112812 * r112817;
        return r112818;
}

↓

double f(double a, double b, double c, double d) {
        double r112819 = a;
        double r112820 = b;
        double r112821 = r112819 * r112820;
        double r112822 = c;
        double r112823 = r112819 * r112822;
        double r112824 = r112821 + r112823;
        double r112825 = d;
        double r112826 = r112819 * r112825;
        double r112827 = r112824 + r112826;
        return r112827;
}

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 2020001 
(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)))