Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 391.0ms

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 r83111 = 2.0;
        double r83112 = 1.0;
        double r83113 = 9.0;
        double r83114 = r83112 / r83113;
        double r83115 = r83112 * r83114;
        double r83116 = r83114 * r83114;
        double r83117 = r83115 + r83116;
        double r83118 = r83114 * r83112;
        double r83119 = r83117 + r83118;
        double r83120 = r83111 * r83119;
        return r83120;
}

↓

double f() {
        double r83121 = 2.0;
        double r83122 = 1.0;
        double r83123 = 9.0;
        double r83124 = r83122 / r83123;
        double r83125 = fma(r83121, r83122, r83124);
        double r83126 = 2.0;
        double r83127 = r83126 / r83123;
        double r83128 = r83125 * r83127;
        double r83129 = r83128 * r83122;
        return r83129;
}

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 2020024 +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))))