Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 408.0ms

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 r45985 = 2.0;
        double r45986 = 1.0;
        double r45987 = 9.0;
        double r45988 = r45986 / r45987;
        double r45989 = r45986 * r45988;
        double r45990 = r45988 * r45988;
        double r45991 = r45989 + r45990;
        double r45992 = r45988 * r45986;
        double r45993 = r45991 + r45992;
        double r45994 = r45985 * r45993;
        return r45994;
}

↓

double f() {
        double r45995 = 2.0;
        double r45996 = 1.0;
        double r45997 = 9.0;
        double r45998 = r45996 / r45997;
        double r45999 = fma(r45995, r45996, r45998);
        double r46000 = 2.0;
        double r46001 = r46000 / r45997;
        double r46002 = r45999 * r46001;
        double r46003 = r46002 * r45996;
        return r46003;
}

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 2020025 +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))))