Average Error: 0.0 → 0.0
Time: 11.9s
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 r7906706 = a;
        double r7906707 = b;
        double r7906708 = c;
        double r7906709 = r7906707 + r7906708;
        double r7906710 = d;
        double r7906711 = r7906709 + r7906710;
        double r7906712 = r7906706 * r7906711;
        return r7906712;
}
↓
double f(double a, double b, double c, double d) {
        double r7906713 = d;
        double r7906714 = a;
        double r7906715 = r7906713 * r7906714;
        double r7906716 = b;
        double r7906717 = c;
        double r7906718 = r7906716 + r7906717;
        double r7906719 = r7906718 * r7906714;
        double r7906720 = r7906715 + r7906719;
        return r7906720;
}

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 2019170 
(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)))