Average Error: 3.6 → 0
Time: 1.4s
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 r78487 = a;
        double r78488 = b;
        double r78489 = c;
        double r78490 = d;
        double r78491 = r78489 + r78490;
        double r78492 = r78488 + r78491;
        double r78493 = r78487 + r78492;
        double r78494 = 2.0;
        double r78495 = r78493 * r78494;
        return r78495;
}
↓
double f(double a, double b, double c, double d) {
        double r78496 = b;
        double r78497 = c;
        double r78498 = r78496 + r78497;
        double r78499 = d;
        double r78500 = a;
        double r78501 = r78499 + r78500;
        double r78502 = r78498 + r78501;
        double r78503 = 2.0;
        double r78504 = r78502 * r78503;
        return r78504;
}

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

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

Reproduce

herbie shell --seed 2020027 +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))