Average Error: 0.0 → 0.0
Time: 7.4s
Precision: 64
\[56789 \le a \le 98765 \land 0.0 \le b \le 1 \land 0.0 \le c \le 0.0016773000000000001 \land 0.0 \le d \le 0.0016773000000000001\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(\left(b + c\right) + d\right) \cdot a\]
a \cdot \left(\left(b + c\right) + d\right)
↓
\left(\left(b + c\right) + d\right) \cdot a
double f(double a, double b, double c, double d) {
        double r81662 = a;
        double r81663 = b;
        double r81664 = c;
        double r81665 = r81663 + r81664;
        double r81666 = d;
        double r81667 = r81665 + r81666;
        double r81668 = r81662 * r81667;
        return r81668;
}
↓
double f(double a, double b, double c, double d) {
        double r81669 = b;
        double r81670 = c;
        double r81671 = r81669 + r81670;
        double r81672 = d;
        double r81673 = r81671 + r81672;
        double r81674 = a;
        double r81675 = r81673 * r81674;
        return r81675;
}

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 *-commutative0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019198 
(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)))