Average Error: 0.0 → 0.0
Time: 12.6s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(\left(b + c\right) + d\right) \cdot a\]
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 r84495 = a;
        double r84496 = b;
        double r84497 = c;
        double r84498 = r84496 + r84497;
        double r84499 = d;
        double r84500 = r84498 + r84499;
        double r84501 = r84495 * r84500;
        return r84501;
}
↓
double f(double a, double b, double c, double d) {
        double r84502 = b;
        double r84503 = c;
        double r84504 = r84502 + r84503;
        double r84505 = d;
        double r84506 = r84504 + r84505;
        double r84507 = a;
        double r84508 = r84506 * r84507;
        return r84508;
}

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 2019195 
(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)))