Expression, p6

Average Error: 3.6 → 2.7

Time: 3.1s

Precision: 64

\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]

Math

\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]

↓

\[\left(a + \left(\left(b + c\right) + d\right)\right) \cdot 2\]

C

double f(double a, double b, double c, double d) {
        double r87564 = a;
        double r87565 = b;
        double r87566 = c;
        double r87567 = d;
        double r87568 = r87566 + r87567;
        double r87569 = r87565 + r87568;
        double r87570 = r87564 + r87569;
        double r87571 = 2.0;
        double r87572 = r87570 * r87571;
        return r87572;
}

↓

double f(double a, double b, double c, double d) {
        double r87573 = a;
        double r87574 = b;
        double r87575 = c;
        double r87576 = r87574 + r87575;
        double r87577 = d;
        double r87578 = r87576 + r87577;
        double r87579 = r87573 + r87578;
        double r87580 = 2.0;
        double r87581 = r87579 * r87580;
        return r87581;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original	3.6
Target	3.8
Herbie	2.7

\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

1. Initial program 3.6

   \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
2. Using strategy rm

3. Applied associate-+r+ 2.7

   \[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]

4. Final simplification 2.7

   \[\leadsto \left(a + \left(\left(b + c\right) + d\right)\right) \cdot 2\]

Reproduce

herbie shell --seed 2020039 
(FPCore (a b c d)
  :name "Expression, p6"
  :precision binary64
  :pre (and (<= -14 a -13) (<= -3 b -2) (<= 3 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2) (* (+ c d) 2))

  (* (+ a (+ b (+ c d))) 2))