Average Error: 3.6 → 0
Time: 7.7s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(d + a\right) + \left(c + b\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(d + a\right) + \left(c + b\right)\right)
double f(double a, double b, double c, double d) {
        double r1839342 = a;
        double r1839343 = b;
        double r1839344 = c;
        double r1839345 = d;
        double r1839346 = r1839344 + r1839345;
        double r1839347 = r1839343 + r1839346;
        double r1839348 = r1839342 + r1839347;
        double r1839349 = 2.0;
        double r1839350 = r1839348 * r1839349;
        return r1839350;
}
↓
double f(double a, double b, double c, double d) {
        double r1839351 = 2.0;
        double r1839352 = d;
        double r1839353 = a;
        double r1839354 = r1839352 + r1839353;
        double r1839355 = c;
        double r1839356 = b;
        double r1839357 = r1839355 + r1839356;
        double r1839358 = r1839354 + r1839357;
        double r1839359 = r1839351 * r1839358;
        return r1839359;
}

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. 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 +-commutative2.7

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

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :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))