Average Error: 3.7 → 0
Time: 6.3s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(b + c\right) + \left(d + a\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(b + c\right) + \left(d + a\right)\right)
double f(double a, double b, double c, double d) {
        double r7727707 = a;
        double r7727708 = b;
        double r7727709 = c;
        double r7727710 = d;
        double r7727711 = r7727709 + r7727710;
        double r7727712 = r7727708 + r7727711;
        double r7727713 = r7727707 + r7727712;
        double r7727714 = 2.0;
        double r7727715 = r7727713 * r7727714;
        return r7727715;
}
↓
double f(double a, double b, double c, double d) {
        double r7727716 = 2.0;
        double r7727717 = b;
        double r7727718 = c;
        double r7727719 = r7727717 + r7727718;
        double r7727720 = d;
        double r7727721 = a;
        double r7727722 = r7727720 + r7727721;
        double r7727723 = r7727719 + r7727722;
        double r7727724 = r7727716 * r7727723;
        return r7727724;
}

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
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. 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 +-commutative2.8

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

  6. Applied associate-+r+0

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

  7. Final simplification0

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

Reproduce

herbie shell --seed 2019158 
(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))