Average Error: 0.0 → 0.0
Time: 9.5s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(\left(b + c\right) + d\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
\left(\left(b + c\right) + d\right) \cdot a
double f(double a, double b, double c, double d) {
        double r70415 = a;
        double r70416 = b;
        double r70417 = c;
        double r70418 = r70416 + r70417;
        double r70419 = d;
        double r70420 = r70418 + r70419;
        double r70421 = r70415 * r70420;
        return r70421;
}
↓
double f(double a, double b, double c, double d) {
        double r70422 = b;
        double r70423 = c;
        double r70424 = r70422 + r70423;
        double r70425 = d;
        double r70426 = r70424 + r70425;
        double r70427 = a;
        double r70428 = r70426 * r70427;
        return r70428;
}

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

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

Reproduce

herbie shell --seed 2019194 
(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)))