Average Error: 3.6 → 2.7
Time: 30.6s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\sqrt[3]{\left(\left(\left(\left(b + c\right) + d\right) + a\right) \cdot \left(\left(\left(b + c\right) + a\right) + d\right)\right) \cdot \left(\left(\left(b + c\right) + d\right) + a\right)} \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\sqrt[3]{\left(\left(\left(\left(b + c\right) + d\right) + a\right) \cdot \left(\left(\left(b + c\right) + a\right) + d\right)\right) \cdot \left(\left(\left(b + c\right) + d\right) + a\right)} \cdot 2
double f(double a, double b, double c, double d) {
        double r11133733 = a;
        double r11133734 = b;
        double r11133735 = c;
        double r11133736 = d;
        double r11133737 = r11133735 + r11133736;
        double r11133738 = r11133734 + r11133737;
        double r11133739 = r11133733 + r11133738;
        double r11133740 = 2.0;
        double r11133741 = r11133739 * r11133740;
        return r11133741;
}
↓
double f(double a, double b, double c, double d) {
        double r11133742 = b;
        double r11133743 = c;
        double r11133744 = r11133742 + r11133743;
        double r11133745 = d;
        double r11133746 = r11133744 + r11133745;
        double r11133747 = a;
        double r11133748 = r11133746 + r11133747;
        double r11133749 = r11133744 + r11133747;
        double r11133750 = r11133749 + r11133745;
        double r11133751 = r11133748 * r11133750;
        double r11133752 = r11133751 * r11133748;
        double r11133753 = cbrt(r11133752);
        double r11133754 = 2.0;
        double r11133755 = r11133753 * r11133754;
        return r11133755;
}

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
Herbie2.7
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.6

    \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
  2. 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 associate-+r+2.7

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

  8. Final simplification2.7

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

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(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))