Average Error: 3.7 → 2.8
Time: 25.9s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\sqrt[3]{\left(\left(\left(a + \left(b + c\right)\right) + d\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(\left(a + \left(b + c\right)\right) + d\right)} \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\sqrt[3]{\left(\left(\left(a + \left(b + c\right)\right) + d\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(\left(a + \left(b + c\right)\right) + d\right)} \cdot 2
double f(double a, double b, double c, double d) {
        double r11472688 = a;
        double r11472689 = b;
        double r11472690 = c;
        double r11472691 = d;
        double r11472692 = r11472690 + r11472691;
        double r11472693 = r11472689 + r11472692;
        double r11472694 = r11472688 + r11472693;
        double r11472695 = 2.0;
        double r11472696 = r11472694 * r11472695;
        return r11472696;
}
↓
double f(double a, double b, double c, double d) {
        double r11472697 = a;
        double r11472698 = b;
        double r11472699 = c;
        double r11472700 = r11472698 + r11472699;
        double r11472701 = r11472697 + r11472700;
        double r11472702 = d;
        double r11472703 = r11472701 + r11472702;
        double r11472704 = r11472700 + r11472702;
        double r11472705 = r11472697 + r11472704;
        double r11472706 = r11472703 * r11472705;
        double r11472707 = r11472706 * r11472703;
        double r11472708 = cbrt(r11472707);
        double r11472709 = 2.0;
        double r11472710 = r11472708 * r11472709;
        return r11472710;
}

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
Target3.9
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. Using strategy rm

  7. Applied associate-+r+2.8

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

  9. Applied associate-+r+2.8

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

  10. Final simplification2.8

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

Reproduce

herbie shell --seed 2019173 
(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))