Average Error: 3.6 → 2.9
Time: 18.4s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\sqrt[3]{{\left(a + \left(\left(b + c\right) + d\right)\right)}^{3}} \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\sqrt[3]{{\left(a + \left(\left(b + c\right) + d\right)\right)}^{3}} \cdot 2
double f(double a, double b, double c, double d) {
        double r64817 = a;
        double r64818 = b;
        double r64819 = c;
        double r64820 = d;
        double r64821 = r64819 + r64820;
        double r64822 = r64818 + r64821;
        double r64823 = r64817 + r64822;
        double r64824 = 2.0;
        double r64825 = r64823 * r64824;
        return r64825;
}
↓
double f(double a, double b, double c, double d) {
        double r64826 = a;
        double r64827 = b;
        double r64828 = c;
        double r64829 = r64827 + r64828;
        double r64830 = d;
        double r64831 = r64829 + r64830;
        double r64832 = r64826 + r64831;
        double r64833 = 3.0;
        double r64834 = pow(r64832, r64833);
        double r64835 = cbrt(r64834);
        double r64836 = 2.0;
        double r64837 = r64835 * r64836;
        return r64837;
}

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
Herbie2.9
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

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. Simplified2.9

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

  7. Final simplification2.9

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(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))