Average Error: 0.0 → 0.0
Time: 35.5s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.001677300000000000058247850986958837893326 \land 0.0 \le d \le 0.001677300000000000058247850986958837893326\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[d \cdot a + \left(b + c\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
d \cdot a + \left(b + c\right) \cdot a
double f(double a, double b, double c, double d) {
        double r5849202 = a;
        double r5849203 = b;
        double r5849204 = c;
        double r5849205 = r5849203 + r5849204;
        double r5849206 = d;
        double r5849207 = r5849205 + r5849206;
        double r5849208 = r5849202 * r5849207;
        return r5849208;
}
↓
double f(double a, double b, double c, double d) {
        double r5849209 = d;
        double r5849210 = a;
        double r5849211 = r5849209 * r5849210;
        double r5849212 = b;
        double r5849213 = c;
        double r5849214 = r5849212 + r5849213;
        double r5849215 = r5849214 * r5849210;
        double r5849216 = r5849211 + r5849215;
        return r5849216;
}

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-lft-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789.0 a 98765.0) (<= 0.0 b 1.0) (<= 0.0 c 0.0016773) (<= 0.0 d 0.0016773))

  :herbie-target
  (+ (* a b) (* a (+ c d)))

  (* a (+ (+ b c) d)))