Average Error: 0.0 → 0.0
Time: 13.9s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(b + c\right) \cdot a + d \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
\left(b + c\right) \cdot a + d \cdot a
double f(double a, double b, double c, double d) {
        double r7166486 = a;
        double r7166487 = b;
        double r7166488 = c;
        double r7166489 = r7166487 + r7166488;
        double r7166490 = d;
        double r7166491 = r7166489 + r7166490;
        double r7166492 = r7166486 * r7166491;
        return r7166492;
}
↓
double f(double a, double b, double c, double d) {
        double r7166493 = b;
        double r7166494 = c;
        double r7166495 = r7166493 + r7166494;
        double r7166496 = a;
        double r7166497 = r7166495 * r7166496;
        double r7166498 = d;
        double r7166499 = r7166498 * r7166496;
        double r7166500 = r7166497 + r7166499;
        return r7166500;
}

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-rgt-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(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)))