Average Error: 0.0 → 0.0
Time: 11.5s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(d + \left(c + b\right)\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
\left(d + \left(c + b\right)\right) \cdot a
double f(double a, double b, double c, double d) {
        double r2602781 = a;
        double r2602782 = b;
        double r2602783 = c;
        double r2602784 = r2602782 + r2602783;
        double r2602785 = d;
        double r2602786 = r2602784 + r2602785;
        double r2602787 = r2602781 * r2602786;
        return r2602787;
}
↓
double f(double a, double b, double c, double d) {
        double r2602788 = d;
        double r2602789 = c;
        double r2602790 = b;
        double r2602791 = r2602789 + r2602790;
        double r2602792 = r2602788 + r2602791;
        double r2602793 = a;
        double r2602794 = r2602792 * r2602793;
        return r2602794;
}

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 *-commutative0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019138 +o rules:numerics
(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)))