Average Error: 3.6 → 2.7
Time: 2.8s
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 r95920 = a;
        double r95921 = b;
        double r95922 = c;
        double r95923 = d;
        double r95924 = r95922 + r95923;
        double r95925 = r95921 + r95924;
        double r95926 = r95920 + r95925;
        double r95927 = 2.0;
        double r95928 = r95926 * r95927;
        return r95928;
}
↓
double f(double a, double b, double c, double d) {
        double r95929 = a;
        double r95930 = b;
        double r95931 = c;
        double r95932 = r95930 + r95931;
        double r95933 = r95929 + r95932;
        double r95934 = d;
        double r95935 = r95933 + r95934;
        double r95936 = 2.0;
        double r95937 = r95935 * r95936;
        return r95937;
}

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

Original3.6
Target3.8
Herbie2.7
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

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. Using strategy rm

  5. Applied associate-+r+2.7

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

  6. Final simplification2.7

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

Reproduce

herbie shell --seed 2020039 +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))