Average Error: 0.0 → 0.0
Time: 12.2s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(d \cdot a + c \cdot a\right) + b \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
\left(d \cdot a + c \cdot a\right) + b \cdot a
double f(double a, double b, double c, double d) {
        double r4907946 = a;
        double r4907947 = b;
        double r4907948 = c;
        double r4907949 = r4907947 + r4907948;
        double r4907950 = d;
        double r4907951 = r4907949 + r4907950;
        double r4907952 = r4907946 * r4907951;
        return r4907952;
}
↓
double f(double a, double b, double c, double d) {
        double r4907953 = d;
        double r4907954 = a;
        double r4907955 = r4907953 * r4907954;
        double r4907956 = c;
        double r4907957 = r4907956 * r4907954;
        double r4907958 = r4907955 + r4907957;
        double r4907959 = b;
        double r4907960 = r4907959 * r4907954;
        double r4907961 = r4907958 + r4907960;
        return r4907961;
}

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

Original0.0
Target0.0
Herbie0.0
\[a \cdot b + a \cdot \left(c + d\right)\]

Derivation

  1. Initial program 0.0

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

  3. Applied distribute-lft-in0.0

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

  5. Applied distribute-rgt-in0.0

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

  6. Applied associate-+l+0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789.0 a 98765.0) (<= 0.0 b 1.0) (<= 0.0 c 0.0016773) (<= 0.0 d 0.0016773))

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

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