Average Error: 0.0 → 0.0
Time: 7.6s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[a \cdot d + \left(c + b\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
a \cdot d + \left(c + b\right) \cdot a
double f(double a, double b, double c, double d) {
        double r1956807 = a;
        double r1956808 = b;
        double r1956809 = c;
        double r1956810 = r1956808 + r1956809;
        double r1956811 = d;
        double r1956812 = r1956810 + r1956811;
        double r1956813 = r1956807 * r1956812;
        return r1956813;
}
↓
double f(double a, double b, double c, double d) {
        double r1956814 = a;
        double r1956815 = d;
        double r1956816 = r1956814 * r1956815;
        double r1956817 = c;
        double r1956818 = b;
        double r1956819 = r1956817 + r1956818;
        double r1956820 = r1956819 * r1956814;
        double r1956821 = r1956816 + r1956820;
        return r1956821;
}

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-rgt-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019154 
(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)))