Expression, p14

Average Error: 0.0 → 0.0

Time: 14.2s

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

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

↓

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

C

double f(double a, double b, double c, double d) {
        double r12636749 = a;
        double r12636750 = b;
        double r12636751 = c;
        double r12636752 = r12636750 + r12636751;
        double r12636753 = d;
        double r12636754 = r12636752 + r12636753;
        double r12636755 = r12636749 * r12636754;
        return r12636755;
}

↓

double f(double a, double b, double c, double d) {
        double r12636756 = a;
        double r12636757 = b;
        double r12636758 = c;
        double r12636759 = r12636757 + r12636758;
        double r12636760 = r12636756 * r12636759;
        double r12636761 = d;
        double r12636762 = r12636756 * r12636761;
        double r12636763 = r12636760 + r12636762;
        return r12636763;
}

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. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019173 
(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)))