Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 407.0ms

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 r69717 = 2.0;
        double r69718 = 1.0;
        double r69719 = 9.0;
        double r69720 = r69718 / r69719;
        double r69721 = r69718 * r69720;
        double r69722 = r69720 * r69720;
        double r69723 = r69721 + r69722;
        double r69724 = r69720 * r69718;
        double r69725 = r69723 + r69724;
        double r69726 = r69717 * r69725;
        return r69726;
}

↓

double f() {
        double r69727 = 2.0;
        double r69728 = 1.0;
        double r69729 = 9.0;
        double r69730 = r69728 / r69729;
        double r69731 = fma(r69727, r69728, r69730);
        double r69732 = 2.0;
        double r69733 = r69732 / r69729;
        double r69734 = r69731 * r69733;
        double r69735 = r69734 * r69728;
        return r69735;
}

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 2020062 +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))))