Average Error: 3.7 → 0
Time: 7.4s
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 r40582 = a;
        double r40583 = b;
        double r40584 = c;
        double r40585 = d;
        double r40586 = r40584 + r40585;
        double r40587 = r40583 + r40586;
        double r40588 = r40582 + r40587;
        double r40589 = 2.0;
        double r40590 = r40588 * r40589;
        return r40590;
}
↓
double f(double a, double b, double c, double d) {
        double r40591 = a;
        double r40592 = d;
        double r40593 = r40591 + r40592;
        double r40594 = b;
        double r40595 = c;
        double r40596 = r40594 + r40595;
        double r40597 = r40593 + r40596;
        double r40598 = 2.0;
        double r40599 = r40597 * r40598;
        return r40599;
}

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. 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. Simplified2.8

    \[\leadsto 2 \cdot \left(1 \cdot \color{blue}{\left(c + \left(\left(b + d\right) + a\right)\right)}\right)\]
  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 2019196 
(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))