Average Error: 0.0 → 0.0
Time: 11.6s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[d \cdot a + \left(b + c\right) \cdot a\]
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 r3143676 = a;
        double r3143677 = b;
        double r3143678 = c;
        double r3143679 = r3143677 + r3143678;
        double r3143680 = d;
        double r3143681 = r3143679 + r3143680;
        double r3143682 = r3143676 * r3143681;
        return r3143682;
}
↓
double f(double a, double b, double c, double d) {
        double r3143683 = d;
        double r3143684 = a;
        double r3143685 = r3143683 * r3143684;
        double r3143686 = b;
        double r3143687 = c;
        double r3143688 = r3143686 + r3143687;
        double r3143689 = r3143688 * r3143684;
        double r3143690 = r3143685 + r3143689;
        return r3143690;
}

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 2019139 
(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)))