Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 370.0ms

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 r89261 = 2.0;
        double r89262 = 1.0;
        double r89263 = 9.0;
        double r89264 = r89262 / r89263;
        double r89265 = r89262 * r89264;
        double r89266 = r89264 * r89264;
        double r89267 = r89265 + r89266;
        double r89268 = r89264 * r89262;
        double r89269 = r89267 + r89268;
        double r89270 = r89261 * r89269;
        return r89270;
}

↓

double f() {
        double r89271 = 2.0;
        double r89272 = 1.0;
        double r89273 = 9.0;
        double r89274 = r89272 / r89273;
        double r89275 = r89271 * r89274;
        double r89276 = r89272 + r89274;
        double r89277 = r89276 + r89272;
        double r89278 = r89275 * r89277;
        return r89278;
}

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 2020007 
(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))))