Average Error: 0.0 → 0.0
Time: 14.6s
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 r5263496 = a;
        double r5263497 = b;
        double r5263498 = c;
        double r5263499 = r5263497 + r5263498;
        double r5263500 = d;
        double r5263501 = r5263499 + r5263500;
        double r5263502 = r5263496 * r5263501;
        return r5263502;
}
↓
double f(double a, double b, double c, double d) {
        double r5263503 = a;
        double r5263504 = d;
        double r5263505 = r5263503 * r5263504;
        double r5263506 = c;
        double r5263507 = b;
        double r5263508 = r5263506 + r5263507;
        double r5263509 = r5263508 * r5263503;
        double r5263510 = r5263505 + r5263509;
        return r5263510;
}

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 2019168 
(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)))