Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 428.0ms

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 r70817 = 2.0;
        double r70818 = 1.0;
        double r70819 = 9.0;
        double r70820 = r70818 / r70819;
        double r70821 = r70818 * r70820;
        double r70822 = r70820 * r70820;
        double r70823 = r70821 + r70822;
        double r70824 = r70820 * r70818;
        double r70825 = r70823 + r70824;
        double r70826 = r70817 * r70825;
        return r70826;
}

↓

double f() {
        double r70827 = 2.0;
        double r70828 = 1.0;
        double r70829 = 9.0;
        double r70830 = r70828 / r70829;
        double r70831 = fma(r70827, r70828, r70830);
        double r70832 = 2.0;
        double r70833 = r70832 / r70829;
        double r70834 = r70831 * r70833;
        double r70835 = r70834 * r70828;
        return r70835;
}

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 2020027 +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))))