Average Error: 0.0 → 0.0
Time: 12.0s
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 r3362680 = a;
        double r3362681 = b;
        double r3362682 = c;
        double r3362683 = r3362681 + r3362682;
        double r3362684 = d;
        double r3362685 = r3362683 + r3362684;
        double r3362686 = r3362680 * r3362685;
        return r3362686;
}
↓
double f(double a, double b, double c, double d) {
        double r3362687 = a;
        double r3362688 = d;
        double r3362689 = r3362687 * r3362688;
        double r3362690 = c;
        double r3362691 = b;
        double r3362692 = r3362690 + r3362691;
        double r3362693 = r3362692 * r3362687;
        double r3362694 = r3362689 + r3362693;
        return r3362694;
}

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 2019135 
(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)))