Average Error: 3.7 → 0
Time: 7.3s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(a + d\right) + \left(b + c\right)\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(\left(a + d\right) + \left(b + c\right)\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r58743 = a;
        double r58744 = b;
        double r58745 = c;
        double r58746 = d;
        double r58747 = r58745 + r58746;
        double r58748 = r58744 + r58747;
        double r58749 = r58743 + r58748;
        double r58750 = 2.0;
        double r58751 = r58749 * r58750;
        return r58751;
}
↓
double f(double a, double b, double c, double d) {
        double r58752 = a;
        double r58753 = d;
        double r58754 = r58752 + r58753;
        double r58755 = b;
        double r58756 = c;
        double r58757 = r58755 + r58756;
        double r58758 = r58754 + r58757;
        double r58759 = 2.0;
        double r58760 = r58758 * r58759;
        return r58760;
}

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. Simplified3.1

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

  4. Applied *-un-lft-identity3.1

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

  5. Applied *-un-lft-identity3.1

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

  6. Applied distribute-lft-out3.1

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

  7. Simplified2.7

    \[\leadsto 2 \cdot \left(1 \cdot \color{blue}{\left(c + \left(\left(b + d\right) + a\right)\right)}\right)\]
  8. Using strategy rm

  9. Applied associate-+l+0.0

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

  10. Simplified0.0

    \[\leadsto 2 \cdot \left(1 \cdot \left(c + \left(b + \color{blue}{\left(a + d\right)}\right)\right)\right)\]
  11. Using strategy rm

  12. Applied associate-+r+0

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

  13. Final simplification0

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

Reproduce

herbie shell --seed 2019174 
(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))