Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 3.4m

Precision: 64

Math

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

↓

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

C

double f() {
        double r110140 = 2.0;
        double r110141 = 1.0;
        double r110142 = 9.0;
        double r110143 = r110141 / r110142;
        double r110144 = r110141 * r110143;
        double r110145 = r110143 * r110143;
        double r110146 = r110144 + r110145;
        double r110147 = r110143 * r110141;
        double r110148 = r110146 + r110147;
        double r110149 = r110140 * r110148;
        return r110149;
}

↓

double f() {
        double r110150 = 2.0;
        double r110151 = 1.0;
        double r110152 = 9.0;
        double r110153 = r110151 / r110152;
        double r110154 = r110151 + r110153;
        double r110155 = r110154 + r110151;
        double r110156 = r110153 * r110155;
        double r110157 = r110150 * r110156;
        return r110157;
}

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. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019208 
(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))))