Average Error: 0.0 → 0.0
Time: 31.9s
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 r5123065 = a;
        double r5123066 = b;
        double r5123067 = c;
        double r5123068 = r5123066 + r5123067;
        double r5123069 = d;
        double r5123070 = r5123068 + r5123069;
        double r5123071 = r5123065 * r5123070;
        return r5123071;
}
↓
double f(double a, double b, double c, double d) {
        double r5123072 = b;
        double r5123073 = c;
        double r5123074 = r5123072 + r5123073;
        double r5123075 = d;
        double r5123076 = r5123074 + r5123075;
        double r5123077 = a;
        double r5123078 = r5123076 * r5123077;
        return r5123078;
}


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 2019102 +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)))