Average Error: 3.6 → 2.8
Time: 13.4s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(\left(b + c\right) + d\right) + a\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(\left(b + c\right) + d\right) + a\right)
double f(double a, double b, double c, double d) {
        double r4055134 = a;
        double r4055135 = b;
        double r4055136 = c;
        double r4055137 = d;
        double r4055138 = r4055136 + r4055137;
        double r4055139 = r4055135 + r4055138;
        double r4055140 = r4055134 + r4055139;
        double r4055141 = 2.0;
        double r4055142 = r4055140 * r4055141;
        return r4055142;
}
↓
double f(double a, double b, double c, double d) {
        double r4055143 = 2.0;
        double r4055144 = b;
        double r4055145 = c;
        double r4055146 = r4055144 + r4055145;
        double r4055147 = d;
        double r4055148 = r4055146 + r4055147;
        double r4055149 = a;
        double r4055150 = r4055148 + r4055149;
        double r4055151 = r4055143 * r4055150;
        return r4055151;
}

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

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+2.8

    \[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]
  4. Using strategy rm

  5. Applied log1p-expm1-u2.8

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(a + \left(\left(b + c\right) + d\right)\right)\right)} \cdot 2\]
  6. Using strategy rm

  7. Applied log1p-expm12.8

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

  8. Final simplification2.8

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

Reproduce

herbie shell --seed 2019134 +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))