Average Error: 3.7 → 2.8
Time: 15.6s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(\left(b + c\right) + d\right) + a\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(\left(b + c\right) + d\right) + a\right)
double f(double a, double b, double c, double d) {
        double r3205506 = a;
        double r3205507 = b;
        double r3205508 = c;
        double r3205509 = d;
        double r3205510 = r3205508 + r3205509;
        double r3205511 = r3205507 + r3205510;
        double r3205512 = r3205506 + r3205511;
        double r3205513 = 2.0;
        double r3205514 = r3205512 * r3205513;
        return r3205514;
}
↓
double f(double a, double b, double c, double d) {
        double r3205515 = 2.0;
        double r3205516 = b;
        double r3205517 = c;
        double r3205518 = r3205516 + r3205517;
        double r3205519 = d;
        double r3205520 = r3205518 + r3205519;
        double r3205521 = a;
        double r3205522 = r3205520 + r3205521;
        double r3205523 = r3205515 * r3205522;
        return r3205523;
}

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 add-cbrt-cube2.9

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

  7. Applied pow32.9

    \[\leadsto \sqrt[3]{\color{blue}{{\left(a + \left(\left(b + c\right) + d\right)\right)}^{3}}} \cdot 2\]

  8. Applied rem-cbrt-cube2.8

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

  9. Final simplification2.8

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :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))