Average Error: 0.0 → 0.0
Time: 12.1s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(d \cdot a + c \cdot a\right) + b \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
\left(d \cdot a + c \cdot a\right) + b \cdot a
double f(double a, double b, double c, double d) {
        double r34723679 = a;
        double r34723680 = b;
        double r34723681 = c;
        double r34723682 = r34723680 + r34723681;
        double r34723683 = d;
        double r34723684 = r34723682 + r34723683;
        double r34723685 = r34723679 * r34723684;
        return r34723685;
}
↓
double f(double a, double b, double c, double d) {
        double r34723686 = d;
        double r34723687 = a;
        double r34723688 = r34723686 * r34723687;
        double r34723689 = c;
        double r34723690 = r34723689 * r34723687;
        double r34723691 = r34723688 + r34723690;
        double r34723692 = b;
        double r34723693 = r34723692 * r34723687;
        double r34723694 = r34723691 + r34723693;
        return r34723694;
}

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. Using strategy rm

  5. Applied distribute-rgt-in0.0

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

  6. Applied associate-+l+0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019119 
(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)))