Expression, p14

Average Error: 0.0 → 0.0

Time: 2.5s

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 r98109 = a;
        double r98110 = b;
        double r98111 = c;
        double r98112 = r98110 + r98111;
        double r98113 = d;
        double r98114 = r98112 + r98113;
        double r98115 = r98109 * r98114;
        return r98115;
}

↓

double f(double a, double b, double c, double d) {
        double r98116 = a;
        double r98117 = b;
        double r98118 = r98116 * r98117;
        double r98119 = c;
        double r98120 = r98116 * r98119;
        double r98121 = r98118 + r98120;
        double r98122 = d;
        double r98123 = r98116 * r98122;
        double r98124 = r98121 + r98123;
        return r98124;
}

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)))