Average Error: 0.0 → 0.0
Time: 8.6s
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 r2231647 = a;
        double r2231648 = b;
        double r2231649 = c;
        double r2231650 = r2231648 + r2231649;
        double r2231651 = d;
        double r2231652 = r2231650 + r2231651;
        double r2231653 = r2231647 * r2231652;
        return r2231653;
}
↓
double f(double a, double b, double c, double d) {
        double r2231654 = a;
        double r2231655 = d;
        double r2231656 = r2231654 * r2231655;
        double r2231657 = c;
        double r2231658 = b;
        double r2231659 = r2231657 + r2231658;
        double r2231660 = r2231659 * r2231654;
        double r2231661 = r2231656 + r2231660;
        return r2231661;
}

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 2019129 
(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)))