Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 3.0s

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 r58028 = 2.0;
        double r58029 = 1.0;
        double r58030 = 9.0;
        double r58031 = r58029 / r58030;
        double r58032 = r58029 * r58031;
        double r58033 = r58031 * r58031;
        double r58034 = r58032 + r58033;
        double r58035 = r58031 * r58029;
        double r58036 = r58034 + r58035;
        double r58037 = r58028 * r58036;
        return r58037;
}

↓

double f() {
        double r58038 = 2.0;
        double r58039 = 1.0;
        double r58040 = 9.0;
        double r58041 = r58039 / r58040;
        double r58042 = r58039 + r58041;
        double r58043 = r58039 + r58042;
        double r58044 = r58041 * r58043;
        double r58045 = r58038 * r58044;
        return r58045;
}

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 2019347 
(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))))