Expression, p14

Average Error: 0.0 → 0.0

Time: 11.2s

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

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

↓

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

C

double f(double a, double b, double c, double d) {
        double r70585 = a;
        double r70586 = b;
        double r70587 = c;
        double r70588 = r70586 + r70587;
        double r70589 = d;
        double r70590 = r70588 + r70589;
        double r70591 = r70585 * r70590;
        return r70591;
}

↓

double f(double a, double b, double c, double d) {
        double r70592 = b;
        double r70593 = c;
        double r70594 = r70592 + r70593;
        double r70595 = a;
        double r70596 = r70594 * r70595;
        double r70597 = d;
        double r70598 = r70597 * r70595;
        double r70599 = r70596 + r70598;
        return r70599;
}

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. Simplified 0.0

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

5. Simplified 0.0

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

6. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019325 
(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)))