Average Error: 0.0 → 0.0
Time: 4.0s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot \left(b + c\right) + a \cdot d\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot \left(b + c\right) + a \cdot d
double f(double a, double b, double c, double d) {
        double r98877 = a;
        double r98878 = b;
        double r98879 = c;
        double r98880 = r98878 + r98879;
        double r98881 = d;
        double r98882 = r98880 + r98881;
        double r98883 = r98877 * r98882;
        return r98883;
}
↓
double f(double a, double b, double c, double d) {
        double r98884 = a;
        double r98885 = b;
        double r98886 = c;
        double r98887 = r98885 + r98886;
        double r98888 = r98884 * r98887;
        double r98889 = d;
        double r98890 = r98884 * r98889;
        double r98891 = r98888 + r98890;
        return r98891;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 
(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)))