Average Error: 3.7 → 0.0
Time: 30.7s
Precision: 64
\[-14.0 \le a \le -13.0 \land -3.0 \le b \le -2.0 \land 3.0 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2.0\]
↓
\[2.0 \cdot \left(\left(b + \left(d + a\right)\right) + c\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2.0
↓
2.0 \cdot \left(\left(b + \left(d + a\right)\right) + c\right)
double f(double a, double b, double c, double d) {
        double r4142419 = a;
        double r4142420 = b;
        double r4142421 = c;
        double r4142422 = d;
        double r4142423 = r4142421 + r4142422;
        double r4142424 = r4142420 + r4142423;
        double r4142425 = r4142419 + r4142424;
        double r4142426 = 2.0;
        double r4142427 = r4142425 * r4142426;
        return r4142427;
}
↓
double f(double a, double b, double c, double d) {
        double r4142428 = 2.0;
        double r4142429 = b;
        double r4142430 = d;
        double r4142431 = a;
        double r4142432 = r4142430 + r4142431;
        double r4142433 = r4142429 + r4142432;
        double r4142434 = c;
        double r4142435 = r4142433 + r4142434;
        double r4142436 = r4142428 * r4142435;
        return r4142436;
}

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
Herbie0.0
\[\left(a + b\right) \cdot 2.0 + \left(c + d\right) \cdot 2.0\]

Derivation

  1. Initial program 3.7

    \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2.0\]
  2. Using strategy rm

  3. Applied associate-+r+2.8

    \[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2.0\]
  4. Using strategy rm

  5. Applied log1p-expm1-u2.8

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(a + \left(\left(b + c\right) + d\right)\right)\right)} \cdot 2.0\]
  6. Using strategy rm

  7. Applied expm1-log1p-u2.8

    \[\leadsto \mathsf{log1p}\left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\mathsf{expm1}\left(a + \left(\left(b + c\right) + d\right)\right)\right)\right)}\right) \cdot 2.0\]

  8. Simplified0.1

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\color{blue}{c + \left(b + \left(a + d\right)\right)}\right)\right) \cdot 2.0\]
  9. Using strategy rm

  10. Applied log1p-expm10.0

    \[\leadsto \color{blue}{\left(c + \left(b + \left(a + d\right)\right)\right)} \cdot 2.0\]

  11. Final simplification0.0

    \[\leadsto 2.0 \cdot \left(\left(b + \left(d + a\right)\right) + c\right)\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :pre (and (<= -14.0 a -13.0) (<= -3.0 b -2.0) (<= 3.0 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2.0) (* (+ c d) 2.0))

  (* (+ a (+ b (+ c d))) 2.0))