Average Error: 3.7 → 2.8
Time: 3.0s
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 r123073 = a;
        double r123074 = b;
        double r123075 = c;
        double r123076 = d;
        double r123077 = r123075 + r123076;
        double r123078 = r123074 + r123077;
        double r123079 = r123073 + r123078;
        double r123080 = 2.0;
        double r123081 = r123079 * r123080;
        return r123081;
}
↓
double f(double a, double b, double c, double d) {
        double r123082 = a;
        double r123083 = b;
        double r123084 = c;
        double r123085 = r123083 + r123084;
        double r123086 = r123082 + r123085;
        double r123087 = d;
        double r123088 = r123086 + r123087;
        double r123089 = 2.0;
        double r123090 = r123088 * r123089;
        return r123090;
}

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
Herbie2.8
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.7

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

  3. Applied associate-+r+2.8

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

  5. Applied associate-+r+2.8

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

  6. Final simplification2.8

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

Reproduce

herbie shell --seed 2019362 +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))