Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 373.0ms

Precision: 64

Math

\[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]

↓

\[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]

C

double f() {
        double r65512 = 2.0;
        double r65513 = 1.0;
        double r65514 = 9.0;
        double r65515 = r65513 / r65514;
        double r65516 = r65513 * r65515;
        double r65517 = r65515 * r65515;
        double r65518 = r65516 + r65517;
        double r65519 = r65515 * r65513;
        double r65520 = r65518 + r65519;
        double r65521 = r65512 * r65520;
        return r65521;
}

↓

double f() {
        double r65522 = 2.0;
        double r65523 = 1.0;
        double r65524 = 9.0;
        double r65525 = r65523 / r65524;
        double r65526 = r65523 * r65525;
        double r65527 = r65525 * r65525;
        double r65528 = r65526 + r65527;
        double r65529 = r65525 * r65523;
        double r65530 = r65528 + r65529;
        double r65531 = r65522 * r65530;
        return r65531;
}

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 2020020 +o rules:numerics
(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))))