Average Error: 3.7 → 2.8
Time: 6.6s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(a + \left(b + c\right)\right) + d\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(\left(a + \left(b + c\right)\right) + d\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r62096 = a;
        double r62097 = b;
        double r62098 = c;
        double r62099 = d;
        double r62100 = r62098 + r62099;
        double r62101 = r62097 + r62100;
        double r62102 = r62096 + r62101;
        double r62103 = 2.0;
        double r62104 = r62102 * r62103;
        return r62104;
}
↓
double f(double a, double b, double c, double d) {
        double r62105 = a;
        double r62106 = b;
        double r62107 = c;
        double r62108 = r62106 + r62107;
        double r62109 = r62105 + r62108;
        double r62110 = d;
        double r62111 = r62109 + r62110;
        double r62112 = 2.0;
        double r62113 = r62111 * r62112;
        return r62113;
}

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 associate-+r+2.8

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

  6. Final simplification2.8

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

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))