Average Error: 3.7 → 2.8
Time: 6.6s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(a + \left(b + c\right)\right) + d\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(\left(a + \left(b + c\right)\right) + d\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r82997 = a;
        double r82998 = b;
        double r82999 = c;
        double r83000 = d;
        double r83001 = r82999 + r83000;
        double r83002 = r82998 + r83001;
        double r83003 = r82997 + r83002;
        double r83004 = 2.0;
        double r83005 = r83003 * r83004;
        return r83005;
}
↓
double f(double a, double b, double c, double d) {
        double r83006 = a;
        double r83007 = b;
        double r83008 = c;
        double r83009 = r83007 + r83008;
        double r83010 = r83006 + r83009;
        double r83011 = d;
        double r83012 = r83010 + r83011;
        double r83013 = 2.0;
        double r83014 = r83012 * r83013;
        return r83014;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.7
Target3.8
Herbie2.8
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

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+2.8

    \[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]
  4. Using strategy rm

  5. Applied associate-+r+2.8

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

  6. Final simplification2.8

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

Reproduce

herbie shell --seed 2020045 +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))