Average Error: 3.7 → 2.8
Time: 11.9s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(a + \left(\left(b + c\right) + d\right)\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(a + \left(\left(b + c\right) + d\right)\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r108769 = a;
        double r108770 = b;
        double r108771 = c;
        double r108772 = d;
        double r108773 = r108771 + r108772;
        double r108774 = r108770 + r108773;
        double r108775 = r108769 + r108774;
        double r108776 = 2.0;
        double r108777 = r108775 * r108776;
        return r108777;
}
↓
double f(double a, double b, double c, double d) {
        double r108778 = a;
        double r108779 = b;
        double r108780 = c;
        double r108781 = r108779 + r108780;
        double r108782 = d;
        double r108783 = r108781 + r108782;
        double r108784 = r108778 + r108783;
        double r108785 = 2.0;
        double r108786 = r108784 * r108785;
        return r108786;
}

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
Herbie2.8
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

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. Simplified2.9

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

  8. Applied rem-cbrt-cube2.8

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

  9. Final simplification2.8

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(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))