Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 1.5s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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 r68352 = 2.0;
        double r68353 = 1.0;
        double r68354 = 9.0;
        double r68355 = r68353 / r68354;
        double r68356 = r68353 * r68355;
        double r68357 = r68355 * r68355;
        double r68358 = r68356 + r68357;
        double r68359 = r68355 * r68353;
        double r68360 = r68358 + r68359;
        double r68361 = r68352 * r68360;
        return r68361;
}

↓

double f() {
        double r68362 = 2.0;
        double r68363 = 1.0;
        double r68364 = 9.0;
        double r68365 = r68363 / r68364;
        double r68366 = r68363 * r68365;
        double r68367 = r68365 * r68365;
        double r68368 = r68366 + r68367;
        double r68369 = r68365 * r68363;
        double r68370 = r68368 + r68369;
        double r68371 = r68362 * r68370;
        return r68371;
}

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 2020046 
(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))))