Average Error: 0.0 → 0.0
Time: 2.0s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.0016773000000000001 \land 0.0 \le d \le 0.0016773000000000001\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot b + a \cdot \left(c + d\right)\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot b + a \cdot \left(c + d\right)
double f(double a, double b, double c, double d) {
        double r83885 = a;
        double r83886 = b;
        double r83887 = c;
        double r83888 = r83886 + r83887;
        double r83889 = d;
        double r83890 = r83888 + r83889;
        double r83891 = r83885 * r83890;
        return r83891;
}
↓
double f(double a, double b, double c, double d) {
        double r83892 = a;
        double r83893 = b;
        double r83894 = r83892 * r83893;
        double r83895 = c;
        double r83896 = d;
        double r83897 = r83895 + r83896;
        double r83898 = r83892 * r83897;
        double r83899 = r83894 + r83898;
        return r83899;
}

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. Using strategy rm

  5. Applied distribute-lft-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020056 
(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)))