Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 378.0ms

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 r61619 = 2.0;
        double r61620 = 1.0;
        double r61621 = 9.0;
        double r61622 = r61620 / r61621;
        double r61623 = r61620 * r61622;
        double r61624 = r61622 * r61622;
        double r61625 = r61623 + r61624;
        double r61626 = r61622 * r61620;
        double r61627 = r61625 + r61626;
        double r61628 = r61619 * r61627;
        return r61628;
}

↓

double f() {
        double r61629 = 2.0;
        double r61630 = 1.0;
        double r61631 = 9.0;
        double r61632 = r61630 / r61631;
        double r61633 = fma(r61629, r61630, r61632);
        double r61634 = 2.0;
        double r61635 = r61634 / r61631;
        double r61636 = r61633 * r61635;
        double r61637 = r61636 * r61630;
        return r61637;
}

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 2020049 +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))))