Average Error: 0.0 → 0.0
Time: 11.5s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[d \cdot a + \left(b + c\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
d \cdot a + \left(b + c\right) \cdot a
double f(double a, double b, double c, double d) {
        double r3738715 = a;
        double r3738716 = b;
        double r3738717 = c;
        double r3738718 = r3738716 + r3738717;
        double r3738719 = d;
        double r3738720 = r3738718 + r3738719;
        double r3738721 = r3738715 * r3738720;
        return r3738721;
}
↓
double f(double a, double b, double c, double d) {
        double r3738722 = d;
        double r3738723 = a;
        double r3738724 = r3738722 * r3738723;
        double r3738725 = b;
        double r3738726 = c;
        double r3738727 = r3738725 + r3738726;
        double r3738728 = r3738727 * r3738723;
        double r3738729 = r3738724 + r3738728;
        return r3738729;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019133 
(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)))