Average Error: 3.7 → 2.8
Time: 2.9s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(a + \left(\left(b + c\right) + d\right)\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(a + \left(\left(b + c\right) + d\right)\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r99207 = a;
        double r99208 = b;
        double r99209 = c;
        double r99210 = d;
        double r99211 = r99209 + r99210;
        double r99212 = r99208 + r99211;
        double r99213 = r99207 + r99212;
        double r99214 = 2.0;
        double r99215 = r99213 * r99214;
        return r99215;
}
↓
double f(double a, double b, double c, double d) {
        double r99216 = a;
        double r99217 = b;
        double r99218 = c;
        double r99219 = r99217 + r99218;
        double r99220 = d;
        double r99221 = r99219 + r99220;
        double r99222 = r99216 + r99221;
        double r99223 = 2.0;
        double r99224 = r99222 * r99223;
        return r99224;
}

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 log1p-expm1-u2.8

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(a + \left(\left(b + c\right) + d\right)\right)\right)} \cdot 2\]
  6. Using strategy rm

  7. Applied log1p-expm12.8

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

  8. Final simplification2.8

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

Reproduce

herbie shell --seed 2020001 +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))