Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 399.0ms

Precision: 64

Math

\[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]

↓

\[\left(\mathsf{fma}\left(2, 1, \frac{1}{9}\right) \cdot \frac{2}{9}\right) \cdot 1\]

C

double f() {
        double r76852 = 2.0;
        double r76853 = 1.0;
        double r76854 = 9.0;
        double r76855 = r76853 / r76854;
        double r76856 = r76853 * r76855;
        double r76857 = r76855 * r76855;
        double r76858 = r76856 + r76857;
        double r76859 = r76855 * r76853;
        double r76860 = r76858 + r76859;
        double r76861 = r76852 * r76860;
        return r76861;
}

↓

double f() {
        double r76862 = 2.0;
        double r76863 = 1.0;
        double r76864 = 9.0;
        double r76865 = r76863 / r76864;
        double r76866 = fma(r76862, r76863, r76865);
        double r76867 = 2.0;
        double r76868 = r76867 / r76864;
        double r76869 = r76866 * r76868;
        double r76870 = r76869 * r76863;
        return r76870;
}

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

   \[\leadsto \color{blue}{\left(\mathsf{fma}\left(2, 1, \frac{1}{9}\right) \cdot \frac{2}{9}\right) \cdot 1}\]

3. Final simplification 0

   \[\leadsto \left(\mathsf{fma}\left(2, 1, \frac{1}{9}\right) \cdot \frac{2}{9}\right) \cdot 1\]

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(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))))