Average Error: 0.0 → 0.0
Time: 13.9s
Precision: 64
\[56789 \le a \le 98765 \land 0 \le b \le 1 \land 0 \le c \le 0.0016773 \land 0 \le d \le 0.0016773\]
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(\left(b + c\right) + d\right) \cdot a\]
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 r4036387 = a;
        double r4036388 = b;
        double r4036389 = c;
        double r4036390 = r4036388 + r4036389;
        double r4036391 = d;
        double r4036392 = r4036390 + r4036391;
        double r4036393 = r4036387 * r4036392;
        return r4036393;
}
↓
double f(double a, double b, double c, double d) {
        double r4036394 = b;
        double r4036395 = c;
        double r4036396 = r4036394 + r4036395;
        double r4036397 = d;
        double r4036398 = r4036396 + r4036397;
        double r4036399 = a;
        double r4036400 = r4036398 * r4036399;
        return r4036400;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019144 +o rules:numerics
(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)))