Average Error: 0.0 → 0.0
Time: 8.4s
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 r61445 = a;
        double r61446 = b;
        double r61447 = c;
        double r61448 = r61446 + r61447;
        double r61449 = d;
        double r61450 = r61448 + r61449;
        double r61451 = r61445 * r61450;
        return r61451;
}
↓
double f(double a, double b, double c, double d) {
        double r61452 = a;
        double r61453 = b;
        double r61454 = c;
        double r61455 = r61453 + r61454;
        double r61456 = d;
        double r61457 = r61455 + r61456;
        double r61458 = r61452 * r61457;
        return r61458;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019209 
(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)))