Average Error: 3.7 → 0
Time: 2.6s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(a + d\right) + \left(b + c\right)\right) \cdot 2\]
\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 r73639 = a;
        double r73640 = b;
        double r73641 = c;
        double r73642 = d;
        double r73643 = r73641 + r73642;
        double r73644 = r73640 + r73643;
        double r73645 = r73639 + r73644;
        double r73646 = 2.0;
        double r73647 = r73645 * r73646;
        return r73647;
}
↓
double f(double a, double b, double c, double d) {
        double r73648 = a;
        double r73649 = d;
        double r73650 = r73648 + r73649;
        double r73651 = b;
        double r73652 = c;
        double r73653 = r73651 + r73652;
        double r73654 = r73650 + r73653;
        double r73655 = 2.0;
        double r73656 = r73654 * r73655;
        return r73656;
}

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. 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 2020047 +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))