Expression, p6

Average Error: 3.7 → 2.7

Time: 6.9s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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

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 r116081 = a;
        double r116082 = b;
        double r116083 = c;
        double r116084 = d;
        double r116085 = r116083 + r116084;
        double r116086 = r116082 + r116085;
        double r116087 = r116081 + r116086;
        double r116088 = 2.0;
        double r116089 = r116087 * r116088;
        return r116089;
}

↓

double f(double a, double b, double c, double d) {
        double r116090 = a;
        double r116091 = b;
        double r116092 = c;
        double r116093 = r116091 + r116092;
        double r116094 = d;
        double r116095 = r116093 + r116094;
        double r116096 = r116090 + r116095;
        double r116097 = 2.0;
        double r116098 = r116096 * r116097;
        return r116098;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original	3.7
Target	3.8
Herbie	2.7

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

Derivation

1. Initial program 3.7

   \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
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 2019350 
(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))