Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 403.0ms

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 r70437 = 2.0;
        double r70438 = 1.0;
        double r70439 = 9.0;
        double r70440 = r70438 / r70439;
        double r70441 = r70438 * r70440;
        double r70442 = r70440 * r70440;
        double r70443 = r70441 + r70442;
        double r70444 = r70440 * r70438;
        double r70445 = r70443 + r70444;
        double r70446 = r70437 * r70445;
        return r70446;
}

↓

double f() {
        double r70447 = 2.0;
        double r70448 = 1.0;
        double r70449 = 9.0;
        double r70450 = r70448 / r70449;
        double r70451 = fma(r70447, r70448, r70450);
        double r70452 = 2.0;
        double r70453 = r70452 / r70449;
        double r70454 = r70451 * r70453;
        double r70455 = r70454 * r70448;
        return r70455;
}

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 2019354 +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))))