Average Error: 0.0 → 0.0
Time: 14.3s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot \left(\left(b + c\right) + d\right)\]
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 r62602 = a;
        double r62603 = b;
        double r62604 = c;
        double r62605 = r62603 + r62604;
        double r62606 = d;
        double r62607 = r62605 + r62606;
        double r62608 = r62602 * r62607;
        return r62608;
}
↓
double f(double a, double b, double c, double d) {
        double r62609 = a;
        double r62610 = b;
        double r62611 = c;
        double r62612 = r62610 + r62611;
        double r62613 = d;
        double r62614 = r62612 + r62613;
        double r62615 = r62609 * r62614;
        return r62615;
}

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 2019326 +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 0.0016773) (<= 0.0 d 0.0016773))

  :herbie-target
  (+ (* a b) (* a (+ c d)))

  (* a (+ (+ b c) d)))