Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 350.0ms

Precision: 64

Math

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

↓

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

C

double f() {
        double r101595 = 2.0;
        double r101596 = 1.0;
        double r101597 = 9.0;
        double r101598 = r101596 / r101597;
        double r101599 = r101596 * r101598;
        double r101600 = r101598 * r101598;
        double r101601 = r101599 + r101600;
        double r101602 = r101598 * r101596;
        double r101603 = r101601 + r101602;
        double r101604 = r101595 * r101603;
        return r101604;
}

↓

double f() {
        double r101605 = 2.0;
        double r101606 = 1.0;
        double r101607 = 9.0;
        double r101608 = r101606 / r101607;
        double r101609 = r101605 * r101608;
        double r101610 = r101606 + r101608;
        double r101611 = r101610 + r101606;
        double r101612 = r101609 * r101611;
        return r101612;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2020056 
(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))))