Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 369.0ms

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 r59861 = 2.0;
        double r59862 = 1.0;
        double r59863 = 9.0;
        double r59864 = r59862 / r59863;
        double r59865 = r59862 * r59864;
        double r59866 = r59864 * r59864;
        double r59867 = r59865 + r59866;
        double r59868 = r59864 * r59862;
        double r59869 = r59867 + r59868;
        double r59870 = r59861 * r59869;
        return r59870;
}

↓

double f() {
        double r59871 = 2.0;
        double r59872 = 1.0;
        double r59873 = 9.0;
        double r59874 = r59872 / r59873;
        double r59875 = r59871 * r59874;
        double r59876 = r59872 + r59874;
        double r59877 = r59876 + r59872;
        double r59878 = r59875 * r59877;
        return r59878;
}

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 2019354 
(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))))