Average Error: 0.0 → 0.0
Time: 9.6s
Precision: 64
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(\left(b + c\right) + d\right) \cdot a\]
double f(double a, double b, double c, double d) {
        double r9104989 = a;
        double r9104990 = b;
        double r9104991 = c;
        double r9104992 = r9104990 + r9104991;
        double r9104993 = d;
        double r9104994 = r9104992 + r9104993;
        double r9104995 = r9104989 * r9104994;
        return r9104995;
}
↓
double f(double a, double b, double c, double d) {
        double r9104996 = b;
        double r9104997 = c;
        double r9104998 = r9104996 + r9104997;
        double r9104999 = d;
        double r9105000 = r9104998 + r9104999;
        double r9105001 = a;
        double r9105002 = r9105000 * r9105001;
        return r9105002;
}


a \cdot \left(\left(b + c\right) + d\right)
↓
\left(\left(b + c\right) + d\right) \cdot a

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

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 2019101 
(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)))