Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 400.0ms

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 r81879 = 2.0;
        double r81880 = 1.0;
        double r81881 = 9.0;
        double r81882 = r81880 / r81881;
        double r81883 = r81880 * r81882;
        double r81884 = r81882 * r81882;
        double r81885 = r81883 + r81884;
        double r81886 = r81882 * r81880;
        double r81887 = r81885 + r81886;
        double r81888 = r81879 * r81887;
        return r81888;
}

↓

double f() {
        double r81889 = 2.0;
        double r81890 = 1.0;
        double r81891 = 9.0;
        double r81892 = r81890 / r81891;
        double r81893 = fma(r81889, r81890, r81892);
        double r81894 = 2.0;
        double r81895 = r81894 / r81891;
        double r81896 = r81893 * r81895;
        double r81897 = r81896 * r81890;
        return r81897;
}

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 2020002 +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))))