Expression, p14

Average Error: 0.0 → 0.0

Time: 11.0s

Precision: 64

\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]

Math

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

↓

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

C

double f(double a, double b, double c, double d) {
        double r2894689 = a;
        double r2894690 = b;
        double r2894691 = c;
        double r2894692 = r2894690 + r2894691;
        double r2894693 = d;
        double r2894694 = r2894692 + r2894693;
        double r2894695 = r2894689 * r2894694;
        return r2894695;
}

↓

double f(double a, double b, double c, double d) {
        double r2894696 = b;
        double r2894697 = a;
        double r2894698 = r2894696 * r2894697;
        double r2894699 = c;
        double r2894700 = r2894699 * r2894697;
        double r2894701 = r2894698 + r2894700;
        double r2894702 = d;
        double r2894703 = r2894702 * r2894697;
        double r2894704 = r2894701 + r2894703;
        return r2894704;
}

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-rgt-in 0.0

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

6. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019132 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789 a 98765) (<= 0 b 1) (<= 0 c 0.0016773) (<= 0 d 0.0016773))

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

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