Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 3.0m

Precision: 64

Math

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

↓

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

C

double f() {
        double r79717 = 2.0;
        double r79718 = 1.0;
        double r79719 = 9.0;
        double r79720 = r79718 / r79719;
        double r79721 = r79718 * r79720;
        double r79722 = r79720 * r79720;
        double r79723 = r79721 + r79722;
        double r79724 = r79720 * r79718;
        double r79725 = r79723 + r79724;
        double r79726 = r79717 * r79725;
        return r79726;
}

↓

double f() {
        double r79727 = 2.0;
        double r79728 = 9.0;
        double r79729 = r79727 / r79728;
        double r79730 = r79727 + r79729;
        double r79731 = r79727 + r79730;
        double r79732 = 1.0;
        double r79733 = r79732 / r79728;
        double r79734 = r79731 * r79733;
        double r79735 = r79734 * r79732;
        return r79735;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019174 
(FPCore ()
  :name "Rectangular parallelepiped of dimension a×b×c"

  :herbie-target
  (+ (+ (* (* (/ 1.0 9.0) 1.0) 2.0) (* 2.0 (* (/ 1.0 9.0) (/ 1.0 9.0)))) (* 2.0 (* 1.0 (/ 1.0 9.0))))

  (* 2.0 (+ (+ (* 1.0 (/ 1.0 9.0)) (* (/ 1.0 9.0) (/ 1.0 9.0))) (* (/ 1.0 9.0) 1.0))))