Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 361.0ms

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 r68860 = 2.0;
        double r68861 = 1.0;
        double r68862 = 9.0;
        double r68863 = r68861 / r68862;
        double r68864 = r68861 * r68863;
        double r68865 = r68863 * r68863;
        double r68866 = r68864 + r68865;
        double r68867 = r68863 * r68861;
        double r68868 = r68866 + r68867;
        double r68869 = r68860 * r68868;
        return r68869;
}

↓

double f() {
        double r68870 = 2.0;
        double r68871 = 1.0;
        double r68872 = 9.0;
        double r68873 = r68871 / r68872;
        double r68874 = r68871 * r68873;
        double r68875 = r68873 * r68873;
        double r68876 = r68874 + r68875;
        double r68877 = r68873 * r68871;
        double r68878 = r68876 + r68877;
        double r68879 = r68870 * r68878;
        return r68879;
}

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 2020039 
(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))))