Average Error: 3.7 → 2.8
Time: 2.7s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(a + \left(\left(b + c\right) + d\right)\right)
double f(double a, double b, double c, double d) {
        double r85584 = a;
        double r85585 = b;
        double r85586 = c;
        double r85587 = d;
        double r85588 = r85586 + r85587;
        double r85589 = r85585 + r85588;
        double r85590 = r85584 + r85589;
        double r85591 = 2.0;
        double r85592 = r85590 * r85591;
        return r85592;
}
↓
double f(double a, double b, double c, double d) {
        double r85593 = 2.0;
        double r85594 = a;
        double r85595 = b;
        double r85596 = c;
        double r85597 = r85595 + r85596;
        double r85598 = d;
        double r85599 = r85597 + r85598;
        double r85600 = r85594 + r85599;
        double r85601 = r85593 * r85600;
        return r85601;
}

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
Herbie2.8
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

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 *-un-lft-identity2.8

    \[\leadsto \color{blue}{\left(1 \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right)} \cdot 2\]

  6. Final simplification2.8

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

Reproduce

herbie shell --seed 2020020 +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))