Average Error: 0.0 → 0.0
Time: 9.5s
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 r3853241 = a;
        double r3853242 = b;
        double r3853243 = c;
        double r3853244 = r3853242 + r3853243;
        double r3853245 = d;
        double r3853246 = r3853244 + r3853245;
        double r3853247 = r3853241 * r3853246;
        return r3853247;
}
↓
double f(double a, double b, double c, double d) {
        double r3853248 = d;
        double r3853249 = c;
        double r3853250 = b;
        double r3853251 = r3853249 + r3853250;
        double r3853252 = r3853248 + r3853251;
        double r3853253 = a;
        double r3853254 = r3853252 * r3853253;
        return r3853254;
}

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. Taylor expanded around inf 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019138 
(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)))