Average Error: 0.0 → 0.0
Time: 5.6s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(\left(b + c\right) + d\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
\left(\left(b + c\right) + d\right) \cdot a
double f(double a, double b, double c, double d) {
        double r74832 = a;
        double r74833 = b;
        double r74834 = c;
        double r74835 = r74833 + r74834;
        double r74836 = d;
        double r74837 = r74835 + r74836;
        double r74838 = r74832 * r74837;
        return r74838;
}
↓
double f(double a, double b, double c, double d) {
        double r74839 = b;
        double r74840 = c;
        double r74841 = r74839 + r74840;
        double r74842 = d;
        double r74843 = r74841 + r74842;
        double r74844 = a;
        double r74845 = r74843 * r74844;
        return r74845;
}

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 *-commutative0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019212 
(FPCore (a b c d)
  :name "Expression, p14"
  :precision binary64
  :pre (and (<= 56789 a 98765) (<= 0.0 b 1) (<= 0.0 c 0.0016773000000000001) (<= 0.0 d 0.0016773000000000001))

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

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