Expression, p14

Average Error: 0.0 → 0.0

Time: 11.6s

Precision: 64

\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.0016773000000000001 \land 0.0 \le d \le 0.0016773000000000001\]

Math

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

↓

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

C

double f(double a, double b, double c, double d) {
        double r99629 = a;
        double r99630 = b;
        double r99631 = c;
        double r99632 = r99630 + r99631;
        double r99633 = d;
        double r99634 = r99632 + r99633;
        double r99635 = r99629 * r99634;
        return r99635;
}

↓

double f(double a, double b, double c, double d) {
        double r99636 = a;
        double r99637 = b;
        double r99638 = r99636 * r99637;
        double r99639 = c;
        double r99640 = r99639 * r99636;
        double r99641 = r99638 + r99640;
        double r99642 = d;
        double r99643 = r99636 * r99642;
        double r99644 = r99641 + r99643;
        return r99644;
}

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. Simplified 0.0

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

7. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019199 +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)))