Average Error: 3.6 → 2.7
Time: 3.1s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(a + \left(b + c\right)\right) + d\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(\left(a + \left(b + c\right)\right) + d\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r78087 = a;
        double r78088 = b;
        double r78089 = c;
        double r78090 = d;
        double r78091 = r78089 + r78090;
        double r78092 = r78088 + r78091;
        double r78093 = r78087 + r78092;
        double r78094 = 2.0;
        double r78095 = r78093 * r78094;
        return r78095;
}
↓
double f(double a, double b, double c, double d) {
        double r78096 = a;
        double r78097 = b;
        double r78098 = c;
        double r78099 = r78097 + r78098;
        double r78100 = r78096 + r78099;
        double r78101 = d;
        double r78102 = r78100 + r78101;
        double r78103 = 2.0;
        double r78104 = r78102 * r78103;
        return r78104;
}

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 associate-+r+2.7

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

  6. Final simplification2.7

    \[\leadsto \left(\left(a + \left(b + c\right)\right) + d\right) \cdot 2\]

Reproduce

herbie shell --seed 2020003 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :precision binary64
  :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))