Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 602.0ms

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 r76062 = 2.0;
        double r76063 = 1.0;
        double r76064 = 9.0;
        double r76065 = r76063 / r76064;
        double r76066 = r76063 * r76065;
        double r76067 = r76065 * r76065;
        double r76068 = r76066 + r76067;
        double r76069 = r76065 * r76063;
        double r76070 = r76068 + r76069;
        double r76071 = r76062 * r76070;
        return r76071;
}

↓

double f() {
        double r76072 = 2.0;
        double r76073 = 1.0;
        double r76074 = 9.0;
        double r76075 = r76073 / r76074;
        double r76076 = r76073 * r76075;
        double r76077 = r76075 * r76075;
        double r76078 = r76076 + r76077;
        double r76079 = r76075 * r76073;
        double r76080 = r76078 + r76079;
        double r76081 = r76072 * r76080;
        return r76081;
}

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 2020083 
(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))))