Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 4.0s

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 r49291 = 2.0;
        double r49292 = 1.0;
        double r49293 = 9.0;
        double r49294 = r49292 / r49293;
        double r49295 = r49292 * r49294;
        double r49296 = r49294 * r49294;
        double r49297 = r49295 + r49296;
        double r49298 = r49294 * r49292;
        double r49299 = r49297 + r49298;
        double r49300 = r49291 * r49299;
        return r49300;
}

↓

double f() {
        double r49301 = 2.0;
        double r49302 = 1.0;
        double r49303 = 9.0;
        double r49304 = r49302 / r49303;
        double r49305 = r49302 + r49304;
        double r49306 = r49302 + r49305;
        double r49307 = r49304 * r49306;
        double r49308 = r49301 * r49307;
        return r49308;
}

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 2019303 
(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))))