Average Error: 0.0 → 0.0
Time: 18.3s
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 r4626983 = a;
        double r4626984 = b;
        double r4626985 = c;
        double r4626986 = r4626984 + r4626985;
        double r4626987 = d;
        double r4626988 = r4626986 + r4626987;
        double r4626989 = r4626983 * r4626988;
        return r4626989;
}
↓
double f(double a, double b, double c, double d) {
        double r4626990 = b;
        double r4626991 = c;
        double r4626992 = r4626990 + r4626991;
        double r4626993 = d;
        double r4626994 = r4626992 + r4626993;
        double r4626995 = a;
        double r4626996 = r4626994 * r4626995;
        return r4626996;
}

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 2019143 +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)))