Expression, p6

Average Error: 3.6 → 2.7

Time: 8.2s

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 r73109 = a;
        double r73110 = b;
        double r73111 = c;
        double r73112 = d;
        double r73113 = r73111 + r73112;
        double r73114 = r73110 + r73113;
        double r73115 = r73109 + r73114;
        double r73116 = 2.0;
        double r73117 = r73115 * r73116;
        return r73117;
}

↓

double f(double a, double b, double c, double d) {
        double r73118 = a;
        double r73119 = b;
        double r73120 = c;
        double r73121 = r73119 + r73120;
        double r73122 = d;
        double r73123 = r73121 + r73122;
        double r73124 = r73118 + r73123;
        double r73125 = 2.0;
        double r73126 = r73124 * r73125;
        return r73126;
}

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 2019291 
(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))