Average Error: 3.7 → 2.8
Time: 8.8s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(a + \left(\left(b + c\right) + d\right)\right)
double f(double a, double b, double c, double d) {
        double r100437 = a;
        double r100438 = b;
        double r100439 = c;
        double r100440 = d;
        double r100441 = r100439 + r100440;
        double r100442 = r100438 + r100441;
        double r100443 = r100437 + r100442;
        double r100444 = 2.0;
        double r100445 = r100443 * r100444;
        return r100445;
}
↓
double f(double a, double b, double c, double d) {
        double r100446 = 2.0;
        double r100447 = a;
        double r100448 = b;
        double r100449 = c;
        double r100450 = r100448 + r100449;
        double r100451 = d;
        double r100452 = r100450 + r100451;
        double r100453 = r100447 + r100452;
        double r100454 = r100446 * r100453;
        return r100454;
}

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 *-un-lft-identity2.8

    \[\leadsto \color{blue}{\left(1 \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right)} \cdot 2\]

  6. Final simplification2.8

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

Reproduce

herbie shell --seed 2019209 +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))