Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 3.4s

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 r48454 = 2.0;
        double r48455 = 1.0;
        double r48456 = 9.0;
        double r48457 = r48455 / r48456;
        double r48458 = r48455 * r48457;
        double r48459 = r48457 * r48457;
        double r48460 = r48458 + r48459;
        double r48461 = r48457 * r48455;
        double r48462 = r48460 + r48461;
        double r48463 = r48454 * r48462;
        return r48463;
}

↓

double f() {
        double r48464 = 2.0;
        double r48465 = 1.0;
        double r48466 = 9.0;
        double r48467 = r48465 / r48466;
        double r48468 = r48465 + r48467;
        double r48469 = r48465 + r48468;
        double r48470 = r48467 * r48469;
        double r48471 = r48464 * r48470;
        return r48471;
}

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 2019325 
(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))))