Average Error: 3.6 → 2.7
Time: 14.9s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\sqrt[3]{\left(\left(\left(\left(b + c\right) + d\right) + a\right) \cdot \left(\left(\left(b + c\right) + a\right) + d\right)\right) \cdot \left(\left(\left(b + c\right) + a\right) + d\right)} \cdot 2\]
\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) + a\right) + d\right)} \cdot 2
double f(double a, double b, double c, double d) {
        double r1866157 = a;
        double r1866158 = b;
        double r1866159 = c;
        double r1866160 = d;
        double r1866161 = r1866159 + r1866160;
        double r1866162 = r1866158 + r1866161;
        double r1866163 = r1866157 + r1866162;
        double r1866164 = 2.0;
        double r1866165 = r1866163 * r1866164;
        return r1866165;
}
↓
double f(double a, double b, double c, double d) {
        double r1866166 = b;
        double r1866167 = c;
        double r1866168 = r1866166 + r1866167;
        double r1866169 = d;
        double r1866170 = r1866168 + r1866169;
        double r1866171 = a;
        double r1866172 = r1866170 + r1866171;
        double r1866173 = r1866168 + r1866171;
        double r1866174 = r1866173 + r1866169;
        double r1866175 = r1866172 * r1866174;
        double r1866176 = r1866175 * r1866174;
        double r1866177 = cbrt(r1866176);
        double r1866178 = 2.0;
        double r1866179 = r1866177 * r1866178;
        return r1866179;
}

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

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

  9. Applied associate-+r+2.7

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

  10. Final simplification2.7

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

Reproduce

herbie shell --seed 2019152 
(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))