Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 395.0ms

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 r54547 = 2.0;
        double r54548 = 1.0;
        double r54549 = 9.0;
        double r54550 = r54548 / r54549;
        double r54551 = r54548 * r54550;
        double r54552 = r54550 * r54550;
        double r54553 = r54551 + r54552;
        double r54554 = r54550 * r54548;
        double r54555 = r54553 + r54554;
        double r54556 = r54547 * r54555;
        return r54556;
}

↓

double f() {
        double r54557 = 2.0;
        double r54558 = 1.0;
        double r54559 = 9.0;
        double r54560 = r54558 / r54559;
        double r54561 = fma(r54557, r54558, r54560);
        double r54562 = 2.0;
        double r54563 = r54562 / r54559;
        double r54564 = r54561 * r54563;
        double r54565 = r54564 * r54558;
        return r54565;
}

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 2020065 +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))))