Average Error: 3.6 → 2.7
Time: 13.2s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\sqrt[3]{\left(\left(d + \left(\left(b + c\right) + a\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\sqrt[3]{\left(\left(d + \left(\left(b + c\right) + a\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
double f(double a, double b, double c, double d) {
        double r1810946 = a;
        double r1810947 = b;
        double r1810948 = c;
        double r1810949 = d;
        double r1810950 = r1810948 + r1810949;
        double r1810951 = r1810947 + r1810950;
        double r1810952 = r1810946 + r1810951;
        double r1810953 = 2.0;
        double r1810954 = r1810952 * r1810953;
        return r1810954;
}
↓
double f(double a, double b, double c, double d) {
        double r1810955 = d;
        double r1810956 = b;
        double r1810957 = c;
        double r1810958 = r1810956 + r1810957;
        double r1810959 = a;
        double r1810960 = r1810958 + r1810959;
        double r1810961 = r1810955 + r1810960;
        double r1810962 = r1810958 + r1810955;
        double r1810963 = r1810959 + r1810962;
        double r1810964 = r1810961 * r1810963;
        double r1810965 = r1810964 * r1810963;
        double r1810966 = cbrt(r1810965);
        double r1810967 = 2.0;
        double r1810968 = r1810966 * r1810967;
        return r1810968;
}

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+2.7

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

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

  8. Final simplification2.7

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

Reproduce

herbie shell --seed 2019129 +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))