Average Error: 3.6 → 0
Time: 6.1s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(c + b\right) + \left(d + a\right)\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(\left(c + b\right) + \left(d + a\right)\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r66732 = a;
        double r66733 = b;
        double r66734 = c;
        double r66735 = d;
        double r66736 = r66734 + r66735;
        double r66737 = r66733 + r66736;
        double r66738 = r66732 + r66737;
        double r66739 = 2.0;
        double r66740 = r66738 * r66739;
        return r66740;
}
↓
double f(double a, double b, double c, double d) {
        double r66741 = c;
        double r66742 = b;
        double r66743 = r66741 + r66742;
        double r66744 = d;
        double r66745 = a;
        double r66746 = r66744 + r66745;
        double r66747 = r66743 + r66746;
        double r66748 = 2.0;
        double r66749 = r66747 * r66748;
        return r66749;
}

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

Original3.6
Target3.8
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.6

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

  2. Simplified3.1

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

  4. Applied flip-+3.6

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

  5. Simplified2.8

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

  6. Simplified2.8

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

  8. Applied *-un-lft-identity2.8

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

  9. Applied times-frac2.7

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

  10. Simplified0

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

  11. Simplified0

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

  12. Final simplification0

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

Reproduce

herbie shell --seed 2019179 
(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))