Average Error: 0.0 → 0.0
Time: 7.6s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot \left(\left(b + c\right) + d\right)\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot \left(\left(b + c\right) + d\right)
double f(double a, double b, double c, double d) {
        double r48949 = a;
        double r48950 = b;
        double r48951 = c;
        double r48952 = r48950 + r48951;
        double r48953 = d;
        double r48954 = r48952 + r48953;
        double r48955 = r48949 * r48954;
        return r48955;
}
↓
double f(double a, double b, double c, double d) {
        double r48956 = a;
        double r48957 = b;
        double r48958 = c;
        double r48959 = r48957 + r48958;
        double r48960 = d;
        double r48961 = r48959 + r48960;
        double r48962 = r48956 * r48961;
        return r48962;
}

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. Using strategy rm

  5. Applied distribute-lft-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019297 
(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)))