Average Error: 0.0 → 0.0
Time: 10.3s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(\left(c + d\right) + b\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
\left(\left(c + d\right) + b\right) \cdot a
double f(double a, double b, double c, double d) {
        double r64609 = a;
        double r64610 = b;
        double r64611 = c;
        double r64612 = r64610 + r64611;
        double r64613 = d;
        double r64614 = r64612 + r64613;
        double r64615 = r64609 * r64614;
        return r64615;
}
↓
double f(double a, double b, double c, double d) {
        double r64616 = c;
        double r64617 = d;
        double r64618 = r64616 + r64617;
        double r64619 = b;
        double r64620 = r64618 + r64619;
        double r64621 = a;
        double r64622 = r64620 * r64621;
        return r64622;
}

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. Using strategy rm

  4. Applied associate-+l+0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019196 +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)))