Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 352.0ms

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 r59747 = 2.0;
        double r59748 = 1.0;
        double r59749 = 9.0;
        double r59750 = r59748 / r59749;
        double r59751 = r59748 * r59750;
        double r59752 = r59750 * r59750;
        double r59753 = r59751 + r59752;
        double r59754 = r59750 * r59748;
        double r59755 = r59753 + r59754;
        double r59756 = r59747 * r59755;
        return r59756;
}

↓

double f() {
        double r59757 = 2.0;
        double r59758 = 1.0;
        double r59759 = 9.0;
        double r59760 = r59758 / r59759;
        double r59761 = r59758 * r59760;
        double r59762 = r59760 * r59760;
        double r59763 = r59761 + r59762;
        double r59764 = r59760 * r59758;
        double r59765 = r59763 + r59764;
        double r59766 = r59757 * r59765;
        return r59766;
}

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 2020059 
(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))))