Average Error: 3.6 → 0
Time: 5.8s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(a + d\right) + \left(b + c\right)\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(\left(a + d\right) + \left(b + c\right)\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r55380 = a;
        double r55381 = b;
        double r55382 = c;
        double r55383 = d;
        double r55384 = r55382 + r55383;
        double r55385 = r55381 + r55384;
        double r55386 = r55380 + r55385;
        double r55387 = 2.0;
        double r55388 = r55386 * r55387;
        return r55388;
}
↓
double f(double a, double b, double c, double d) {
        double r55389 = a;
        double r55390 = d;
        double r55391 = r55389 + r55390;
        double r55392 = b;
        double r55393 = c;
        double r55394 = r55392 + r55393;
        double r55395 = r55391 + r55394;
        double r55396 = 2.0;
        double r55397 = r55395 * r55396;
        return r55397;
}

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
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.6

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

  2. Taylor expanded around 0 2.8

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

  4. Applied associate-+r+0

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

  5. Final simplification0

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

Reproduce

herbie shell --seed 2019323 +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))