Average Error: 0.0 → 0.0
Time: 16.8s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(d + \left(c + b\right)\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
\left(d + \left(c + b\right)\right) \cdot a
double f(double a, double b, double c, double d) {
        double r60516 = a;
        double r60517 = b;
        double r60518 = c;
        double r60519 = r60517 + r60518;
        double r60520 = d;
        double r60521 = r60519 + r60520;
        double r60522 = r60516 * r60521;
        return r60522;
}
↓
double f(double a, double b, double c, double d) {
        double r60523 = d;
        double r60524 = c;
        double r60525 = b;
        double r60526 = r60524 + r60525;
        double r60527 = r60523 + r60526;
        double r60528 = a;
        double r60529 = r60527 * r60528;
        return r60529;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(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)))