Average Error: 3.7 → 2.7
Time: 50.1s
Precision: 64
\[-14.0 \le a \le -13.0 \land -3.0 \le b \le -2.0 \land 3.0 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2.0\]
↓
\[\sqrt[3]{\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(\left(d + \left(\left(b + c\right) + a\right)\right) \cdot \left(d + \left(\left(b + c\right) + a\right)\right)\right)} \cdot 2.0\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2.0
↓
\sqrt[3]{\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(\left(d + \left(\left(b + c\right) + a\right)\right) \cdot \left(d + \left(\left(b + c\right) + a\right)\right)\right)} \cdot 2.0
double f(double a, double b, double c, double d) {
        double r5479061 = a;
        double r5479062 = b;
        double r5479063 = c;
        double r5479064 = d;
        double r5479065 = r5479063 + r5479064;
        double r5479066 = r5479062 + r5479065;
        double r5479067 = r5479061 + r5479066;
        double r5479068 = 2.0;
        double r5479069 = r5479067 * r5479068;
        return r5479069;
}
↓
double f(double a, double b, double c, double d) {
        double r5479070 = a;
        double r5479071 = b;
        double r5479072 = c;
        double r5479073 = r5479071 + r5479072;
        double r5479074 = d;
        double r5479075 = r5479073 + r5479074;
        double r5479076 = r5479070 + r5479075;
        double r5479077 = r5479073 + r5479070;
        double r5479078 = r5479074 + r5479077;
        double r5479079 = r5479078 * r5479078;
        double r5479080 = r5479076 * r5479079;
        double r5479081 = cbrt(r5479080);
        double r5479082 = 2.0;
        double r5479083 = r5479081 * r5479082;
        return r5479083;
}

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
Target3.8
Herbie2.7
\[\left(a + b\right) \cdot 2.0 + \left(c + d\right) \cdot 2.0\]

Derivation

  1. Initial program 3.7

    \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2.0\]
  2. Using strategy rm

  3. Applied associate-+r+2.8

    \[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2.0\]
  4. Using strategy rm

  5. Applied add-cbrt-cube2.9

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)}} \cdot 2.0\]
  6. Using strategy rm

  7. Applied associate-+r+2.7

    \[\leadsto \sqrt[3]{\left(\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \color{blue}{\left(\left(a + \left(b + c\right)\right) + d\right)}\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2.0\]
  8. Using strategy rm

  9. Applied associate-+r+2.7

    \[\leadsto \sqrt[3]{\left(\color{blue}{\left(\left(a + \left(b + c\right)\right) + d\right)} \cdot \left(\left(a + \left(b + c\right)\right) + d\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2.0\]

  10. Final simplification2.7

    \[\leadsto \sqrt[3]{\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(\left(d + \left(\left(b + c\right) + a\right)\right) \cdot \left(d + \left(\left(b + c\right) + a\right)\right)\right)} \cdot 2.0\]

Reproduce

herbie shell --seed 2019165 
(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))