Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 361.0ms

Precision: 64

Math

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

↓

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

C

double f() {
        double r58607 = 2.0;
        double r58608 = 1.0;
        double r58609 = 9.0;
        double r58610 = r58608 / r58609;
        double r58611 = r58608 * r58610;
        double r58612 = r58610 * r58610;
        double r58613 = r58611 + r58612;
        double r58614 = r58610 * r58608;
        double r58615 = r58613 + r58614;
        double r58616 = r58607 * r58615;
        return r58616;
}

↓

double f() {
        double r58617 = 2.0;
        double r58618 = 1.0;
        double r58619 = 9.0;
        double r58620 = r58618 / r58619;
        double r58621 = r58618 * r58620;
        double r58622 = r58620 * r58620;
        double r58623 = r58621 + r58622;
        double r58624 = r58620 * r58618;
        double r58625 = r58623 + r58624;
        double r58626 = r58617 * r58625;
        return r58626;
}

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. Final simplification 0

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

Reproduce

herbie shell --seed 2020049 
(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))))