Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 3.5s

Precision: 64

Math

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

↓

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

C

double f() {
        double r75271 = 2.0;
        double r75272 = 1.0;
        double r75273 = 9.0;
        double r75274 = r75272 / r75273;
        double r75275 = r75272 * r75274;
        double r75276 = r75274 * r75274;
        double r75277 = r75275 + r75276;
        double r75278 = r75274 * r75272;
        double r75279 = r75277 + r75278;
        double r75280 = r75271 * r75279;
        return r75280;
}

↓

double f() {
        double r75281 = 2.0;
        double r75282 = 1.0;
        double r75283 = 9.0;
        double r75284 = r75282 / r75283;
        double r75285 = r75282 + r75284;
        double r75286 = r75282 + r75285;
        double r75287 = r75284 * r75286;
        double r75288 = r75281 * r75287;
        return r75288;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019322 
(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))))