Average Error: 0.0 → 0.0
Time: 8.0s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.0016773000000000001 \land 0.0 \le d \le 0.0016773000000000001\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot d + a \cdot \left(b + c\right)\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot d + a \cdot \left(b + c\right)
double f(double a, double b, double c, double d) {
        double r127970 = a;
        double r127971 = b;
        double r127972 = c;
        double r127973 = r127971 + r127972;
        double r127974 = d;
        double r127975 = r127973 + r127974;
        double r127976 = r127970 * r127975;
        return r127976;
}
↓
double f(double a, double b, double c, double d) {
        double r127977 = a;
        double r127978 = d;
        double r127979 = r127977 * r127978;
        double r127980 = b;
        double r127981 = c;
        double r127982 = r127980 + r127981;
        double r127983 = r127977 * r127982;
        double r127984 = r127979 + r127983;
        return r127984;
}

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 distribute-lft-in0.0

    \[\leadsto \color{blue}{a \cdot \left(b + c\right) + a \cdot d}\]
  4. Using strategy rm

  5. Applied +-commutative0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 
(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)))