Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 371.0ms

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 r71511 = 2.0;
        double r71512 = 1.0;
        double r71513 = 9.0;
        double r71514 = r71512 / r71513;
        double r71515 = r71512 * r71514;
        double r71516 = r71514 * r71514;
        double r71517 = r71515 + r71516;
        double r71518 = r71514 * r71512;
        double r71519 = r71517 + r71518;
        double r71520 = r71511 * r71519;
        return r71520;
}

↓

double f() {
        double r71521 = 2.0;
        double r71522 = 1.0;
        double r71523 = 9.0;
        double r71524 = r71522 / r71523;
        double r71525 = r71521 * r71524;
        double r71526 = r71522 + r71524;
        double r71527 = r71526 + r71522;
        double r71528 = r71525 * r71527;
        return r71528;
}

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 2020001 
(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))))