Average Error: 3.7 → 0
Time: 1.6s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(b + c\right) + \left(d + a\right)\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(\left(b + c\right) + \left(d + a\right)\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r77449 = a;
        double r77450 = b;
        double r77451 = c;
        double r77452 = d;
        double r77453 = r77451 + r77452;
        double r77454 = r77450 + r77453;
        double r77455 = r77449 + r77454;
        double r77456 = 2.0;
        double r77457 = r77455 * r77456;
        return r77457;
}
↓
double f(double a, double b, double c, double d) {
        double r77458 = b;
        double r77459 = c;
        double r77460 = r77458 + r77459;
        double r77461 = d;
        double r77462 = a;
        double r77463 = r77461 + r77462;
        double r77464 = r77460 + r77463;
        double r77465 = 2.0;
        double r77466 = r77464 * r77465;
        return r77466;
}

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

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 +-commutative2.8

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

  7. Applied associate-+l+0

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

  8. Final simplification0

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

Reproduce

herbie shell --seed 2020089 +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))