Average Error: 3.7 → 0
Time: 2.6s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(a + d\right) + \left(b + c\right)\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(\left(a + d\right) + \left(b + c\right)\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r60982 = a;
        double r60983 = b;
        double r60984 = c;
        double r60985 = d;
        double r60986 = r60984 + r60985;
        double r60987 = r60983 + r60986;
        double r60988 = r60982 + r60987;
        double r60989 = 2.0;
        double r60990 = r60988 * r60989;
        return r60990;
}
↓
double f(double a, double b, double c, double d) {
        double r60991 = a;
        double r60992 = d;
        double r60993 = r60991 + r60992;
        double r60994 = b;
        double r60995 = c;
        double r60996 = r60994 + r60995;
        double r60997 = r60993 + r60996;
        double r60998 = 2.0;
        double r60999 = r60997 * r60998;
        return r60999;
}

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
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.7

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

  2. Taylor expanded around 0 2.8

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

  4. Applied associate-+r+0

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

  5. Final simplification0

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

Reproduce

herbie shell --seed 2020045 
(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))