Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 643.0ms

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 r62671 = 2.0;
        double r62672 = 1.0;
        double r62673 = 9.0;
        double r62674 = r62672 / r62673;
        double r62675 = r62672 * r62674;
        double r62676 = r62674 * r62674;
        double r62677 = r62675 + r62676;
        double r62678 = r62674 * r62672;
        double r62679 = r62677 + r62678;
        double r62680 = r62671 * r62679;
        return r62680;
}

↓

double f() {
        double r62681 = 2.0;
        double r62682 = 1.0;
        double r62683 = 9.0;
        double r62684 = r62682 / r62683;
        double r62685 = fma(r62681, r62682, r62684);
        double r62686 = 2.0;
        double r62687 = r62686 / r62683;
        double r62688 = r62685 * r62687;
        double r62689 = r62688 * r62682;
        return r62689;
}

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 2020083 +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))))