Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 3.4m

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 r95669 = 2.0;
        double r95670 = 1.0;
        double r95671 = 9.0;
        double r95672 = r95670 / r95671;
        double r95673 = r95670 * r95672;
        double r95674 = r95672 * r95672;
        double r95675 = r95673 + r95674;
        double r95676 = r95672 * r95670;
        double r95677 = r95675 + r95676;
        double r95678 = r95669 * r95677;
        return r95678;
}

↓

double f() {
        double r95679 = 2.0;
        double r95680 = 1.0;
        double r95681 = 9.0;
        double r95682 = r95680 / r95681;
        double r95683 = r95680 * r95682;
        double r95684 = r95682 * r95682;
        double r95685 = r95683 + r95684;
        double r95686 = r95682 * r95680;
        double r95687 = r95685 + r95686;
        double r95688 = r95679 * r95687;
        return r95688;
}

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 2019209 
(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))))