Average Error: 0.0 → 0.0
Time: 10.3s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(b + c\right) \cdot a + a \cdot d\]
a \cdot \left(\left(b + c\right) + d\right)
↓
\left(b + c\right) \cdot a + a \cdot d
double f(double a, double b, double c, double d) {
        double r84735 = a;
        double r84736 = b;
        double r84737 = c;
        double r84738 = r84736 + r84737;
        double r84739 = d;
        double r84740 = r84738 + r84739;
        double r84741 = r84735 * r84740;
        return r84741;
}
↓
double f(double a, double b, double c, double d) {
        double r84742 = b;
        double r84743 = c;
        double r84744 = r84742 + r84743;
        double r84745 = a;
        double r84746 = r84744 * r84745;
        double r84747 = d;
        double r84748 = r84745 * r84747;
        double r84749 = r84746 + r84748;
        return r84749;
}

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(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)))