Expression, p14

Average Error: 0.0 → 0.0

Time: 9.6s

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

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

↓

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

C

double f(double a, double b, double c, double d) {
        double r4044574 = a;
        double r4044575 = b;
        double r4044576 = c;
        double r4044577 = r4044575 + r4044576;
        double r4044578 = d;
        double r4044579 = r4044577 + r4044578;
        double r4044580 = r4044574 * r4044579;
        return r4044580;
}

↓

double f(double a, double b, double c, double d) {
        double r4044581 = b;
        double r4044582 = c;
        double r4044583 = r4044581 + r4044582;
        double r4044584 = d;
        double r4044585 = r4044583 + r4044584;
        double r4044586 = a;
        double r4044587 = r4044585 * r4044586;
        return r4044587;
}

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-rgt-in 0.0

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

5. Applied distribute-rgt-out 0.0

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

6. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789.0 a 98765.0) (<= 0.0 b 1.0) (<= 0.0 c 0.0016773) (<= 0.0 d 0.0016773))

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

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