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 r101607 = 2.0;
        double r101608 = 1.0;
        double r101609 = 9.0;
        double r101610 = r101608 / r101609;
        double r101611 = r101608 * r101610;
        double r101612 = r101610 * r101610;
        double r101613 = r101611 + r101612;
        double r101614 = r101610 * r101608;
        double r101615 = r101613 + r101614;
        double r101616 = r101607 * r101615;
        return r101616;
}

↓

double f() {
        double r101617 = 2.0;
        double r101618 = 1.0;
        double r101619 = 9.0;
        double r101620 = r101618 / r101619;
        double r101621 = r101618 + r101620;
        double r101622 = r101618 + r101621;
        double r101623 = r101620 * r101622;
        double r101624 = r101617 * r101623;
        return r101624;
}

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 2019304 
(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))))