Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 652.0ms

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 r80299 = 2.0;
        double r80300 = 1.0;
        double r80301 = 9.0;
        double r80302 = r80300 / r80301;
        double r80303 = r80300 * r80302;
        double r80304 = r80302 * r80302;
        double r80305 = r80303 + r80304;
        double r80306 = r80302 * r80300;
        double r80307 = r80305 + r80306;
        double r80308 = r80299 * r80307;
        return r80308;
}

↓

double f() {
        double r80309 = 2.0;
        double r80310 = 1.0;
        double r80311 = 9.0;
        double r80312 = r80310 / r80311;
        double r80313 = fma(r80309, r80310, r80312);
        double r80314 = 2.0;
        double r80315 = r80314 / r80311;
        double r80316 = r80313 * r80315;
        double r80317 = r80316 * r80310;
        return r80317;
}

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 2020100 +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))))