Average Error: 3.7 → 2.8
Time: 7.0s
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 r104588 = a;
        double r104589 = b;
        double r104590 = c;
        double r104591 = d;
        double r104592 = r104590 + r104591;
        double r104593 = r104589 + r104592;
        double r104594 = r104588 + r104593;
        double r104595 = 2.0;
        double r104596 = r104594 * r104595;
        return r104596;
}
↓
double f(double a, double b, double c, double d) {
        double r104597 = 2.0;
        double r104598 = b;
        double r104599 = c;
        double r104600 = r104598 + r104599;
        double r104601 = d;
        double r104602 = r104600 + r104601;
        double r104603 = a;
        double r104604 = r104602 + r104603;
        double r104605 = r104597 * r104604;
        return r104605;
}

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 pow12.8

    \[\leadsto \color{blue}{{\left(a + \left(\left(b + c\right) + d\right)\right)}^{1}} \cdot 2\]

  6. Final simplification2.8

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

Reproduce

herbie shell --seed 2020047 +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))