Average Error: 3.7 → 0
Time: 4.7s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(b + \left(c + \left(a + d\right)\right)\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(b + \left(c + \left(a + d\right)\right)\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r69707 = a;
        double r69708 = b;
        double r69709 = c;
        double r69710 = d;
        double r69711 = r69709 + r69710;
        double r69712 = r69708 + r69711;
        double r69713 = r69707 + r69712;
        double r69714 = 2.0;
        double r69715 = r69713 * r69714;
        return r69715;
}
↓
double f(double a, double b, double c, double d) {
        double r69716 = b;
        double r69717 = c;
        double r69718 = a;
        double r69719 = d;
        double r69720 = r69718 + r69719;
        double r69721 = r69717 + r69720;
        double r69722 = r69716 + r69721;
        double r69723 = 2.0;
        double r69724 = r69722 * r69723;
        return r69724;
}

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
Target3.9
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. Simplified3.7

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

  4. Applied associate-+l+3.5

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

  5. Simplified0

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

  6. Final simplification0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :pre (and (<= -14.0 a -13.0) (<= -3.0 b -2.0) (<= 3.0 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2.0) (* (+ c d) 2.0))

  (* (+ a (+ b (+ c d))) 2.0))