Average Error: 3.7 → 0
Time: 16.7s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(a + d\right) + \left(c + b\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(a + d\right) + \left(c + b\right)\right)
double f(double a, double b, double c, double d) {
        double r4292851 = a;
        double r4292852 = b;
        double r4292853 = c;
        double r4292854 = d;
        double r4292855 = r4292853 + r4292854;
        double r4292856 = r4292852 + r4292855;
        double r4292857 = r4292851 + r4292856;
        double r4292858 = 2.0;
        double r4292859 = r4292857 * r4292858;
        return r4292859;
}
↓
double f(double a, double b, double c, double d) {
        double r4292860 = 2.0;
        double r4292861 = a;
        double r4292862 = d;
        double r4292863 = r4292861 + r4292862;
        double r4292864 = c;
        double r4292865 = b;
        double r4292866 = r4292864 + r4292865;
        double r4292867 = r4292863 + r4292866;
        double r4292868 = r4292860 * r4292867;
        return r4292868;
}

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 add-cbrt-cube2.9

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

  7. Applied add-cbrt-cube3.0

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

  8. Simplified0.6

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

  10. Applied pow30.6

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\left(b + c\right) + \left(a + d\right)\right)}^{3}}} \cdot 2\]

  11. Applied rem-cbrt-cube0

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

  12. Final simplification0

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

Reproduce

herbie shell --seed 2019163 
(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))