Average Error: 0.0 → 0.0
Time: 15.5s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot b + \left(c + d\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot b + \left(c + d\right) \cdot a
double f(double a, double b, double c, double d) {
        double r9055599 = a;
        double r9055600 = b;
        double r9055601 = c;
        double r9055602 = r9055600 + r9055601;
        double r9055603 = d;
        double r9055604 = r9055602 + r9055603;
        double r9055605 = r9055599 * r9055604;
        return r9055605;
}
↓
double f(double a, double b, double c, double d) {
        double r9055606 = a;
        double r9055607 = b;
        double r9055608 = r9055606 * r9055607;
        double r9055609 = c;
        double r9055610 = d;
        double r9055611 = r9055609 + r9055610;
        double r9055612 = r9055611 * r9055606;
        double r9055613 = r9055608 + r9055612;
        return r9055613;
}

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 associate-+l+0.0

    \[\leadsto a \cdot \color{blue}{\left(b + \left(c + d\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{a \cdot b + a \cdot \left(c + d\right)}\]

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789 a 98765) (<= 0 b 1) (<= 0 c 0.0016773) (<= 0 d 0.0016773))

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

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