Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 5.1m

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 r64540 = 2.0;
        double r64541 = 1.0;
        double r64542 = 9.0;
        double r64543 = r64541 / r64542;
        double r64544 = r64541 * r64543;
        double r64545 = r64543 * r64543;
        double r64546 = r64544 + r64545;
        double r64547 = r64543 * r64541;
        double r64548 = r64546 + r64547;
        double r64549 = r64540 * r64548;
        return r64549;
}

↓

double f() {
        double r64550 = 2.0;
        double r64551 = 1.0;
        double r64552 = 9.0;
        double r64553 = r64551 / r64552;
        double r64554 = r64551 * r64553;
        double r64555 = r64553 * r64553;
        double r64556 = r64554 + r64555;
        double r64557 = r64553 * r64551;
        double r64558 = r64556 + r64557;
        double r64559 = r64550 * r64558;
        return r64559;
}

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 2019209 +o rules:numerics
(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))))