Average Error: 3.6 → 0
Time: 46.5s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(b + c\right) + \left(d + a\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(b + c\right) + \left(d + a\right)\right)
double f(double a, double b, double c, double d) {
        double r19958091 = a;
        double r19958092 = b;
        double r19958093 = c;
        double r19958094 = d;
        double r19958095 = r19958093 + r19958094;
        double r19958096 = r19958092 + r19958095;
        double r19958097 = r19958091 + r19958096;
        double r19958098 = 2.0;
        double r19958099 = r19958097 * r19958098;
        return r19958099;
}
↓
double f(double a, double b, double c, double d) {
        double r19958100 = 2.0;
        double r19958101 = b;
        double r19958102 = c;
        double r19958103 = r19958101 + r19958102;
        double r19958104 = d;
        double r19958105 = a;
        double r19958106 = r19958104 + r19958105;
        double r19958107 = r19958103 + r19958106;
        double r19958108 = r19958100 * r19958107;
        return r19958108;
}

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
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

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+2.7

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

  5. Applied add-cbrt-cube2.9

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)}} \cdot 2\]
  6. Using strategy rm

  7. Applied log1p-expm1-u2.9

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\left(\mathsf{expm1}\left(\left(\sqrt[3]{\left(\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)}\right)\right)\right)\right)} \cdot 2\]

  8. Simplified0.1

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

  10. Applied log1p-expm10

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

  11. Final simplification0

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

Reproduce

herbie shell --seed 2019128 +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))