Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 5.6s

Precision: 64

Math

\[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]

↓

\[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]

C

double f() {
        double r47140 = 2.0;
        double r47141 = 1.0;
        double r47142 = 9.0;
        double r47143 = r47141 / r47142;
        double r47144 = r47141 * r47143;
        double r47145 = r47143 * r47143;
        double r47146 = r47144 + r47145;
        double r47147 = r47143 * r47141;
        double r47148 = r47146 + r47147;
        double r47149 = r47140 * r47148;
        return r47149;
}

↓

double f() {
        double r47150 = 2.0;
        double r47151 = 1.0;
        double r47152 = 9.0;
        double r47153 = r47151 / r47152;
        double r47154 = r47151 * r47153;
        double r47155 = r47153 * r47153;
        double r47156 = r47154 + r47155;
        double r47157 = r47153 * r47151;
        double r47158 = r47156 + r47157;
        double r47159 = r47150 * r47158;
        return r47159;
}

Target

Original	0
Target	0
Herbie	0

\[\left(\left(\frac{1}{9} \cdot 1\right) \cdot 2 + 2 \cdot \left(\frac{1}{9} \cdot \frac{1}{9}\right)\right) + 2 \cdot \left(1 \cdot \frac{1}{9}\right)\]

Derivation

1. Initial program 0

   \[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]

2. Final simplification 0

   \[\leadsto 2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore ()
  :name "Rectangular parallelepiped of dimension a×b×c"
  :precision binary64

  :herbie-target
  (+ (+ (* (* (/ 1 9) 1) 2) (* 2 (* (/ 1 9) (/ 1 9)))) (* 2 (* 1 (/ 1 9))))

  (* 2 (+ (+ (* 1 (/ 1 9)) (* (/ 1 9) (/ 1 9))) (* (/ 1 9) 1))))