Expression, p6

Average Error: 3.6 → 2.8

Time: 3.5s

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 r117892 = a;
        double r117893 = b;
        double r117894 = c;
        double r117895 = d;
        double r117896 = r117894 + r117895;
        double r117897 = r117893 + r117896;
        double r117898 = r117892 + r117897;
        double r117899 = 2.0;
        double r117900 = r117898 * r117899;
        return r117900;
}

↓

double f(double a, double b, double c, double d) {
        double r117901 = a;
        double r117902 = b;
        double r117903 = c;
        double r117904 = r117902 + r117903;
        double r117905 = d;
        double r117906 = r117904 + r117905;
        double r117907 = r117901 + r117906;
        double r117908 = 2.0;
        double r117909 = r117907 * r117908;
        return r117909;
}

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	2.8

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

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+ 2.8

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

4. Final simplification 2.8

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

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(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))