Average Error: 3.7 → 0
Time: 2.8s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(a + d\right) + \left(b + c\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(a + d\right) + \left(b + c\right)\right)
double f(double a, double b, double c, double d) {
        double r111785 = a;
        double r111786 = b;
        double r111787 = c;
        double r111788 = d;
        double r111789 = r111787 + r111788;
        double r111790 = r111786 + r111789;
        double r111791 = r111785 + r111790;
        double r111792 = 2.0;
        double r111793 = r111791 * r111792;
        return r111793;
}
↓
double f(double a, double b, double c, double d) {
        double r111794 = 2.0;
        double r111795 = a;
        double r111796 = d;
        double r111797 = r111795 + r111796;
        double r111798 = b;
        double r111799 = c;
        double r111800 = r111798 + r111799;
        double r111801 = r111797 + r111800;
        double r111802 = r111794 * r111801;
        return r111802;
}

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 *-un-lft-identity3.7

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

  4. Applied *-un-lft-identity3.7

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

  5. Applied distribute-lft-out3.7

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

  6. Simplified2.8

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

  8. Applied distribute-rgt-in2.8

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

  9. Applied associate-+r+0

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

  10. Simplified0

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

  11. Final simplification0

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

Reproduce

herbie shell --seed 2020046 
(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))