Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 398.0ms

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 r67909 = 2.0;
        double r67910 = 1.0;
        double r67911 = 9.0;
        double r67912 = r67910 / r67911;
        double r67913 = r67910 * r67912;
        double r67914 = r67912 * r67912;
        double r67915 = r67913 + r67914;
        double r67916 = r67912 * r67910;
        double r67917 = r67915 + r67916;
        double r67918 = r67909 * r67917;
        return r67918;
}

↓

double f() {
        double r67919 = 2.0;
        double r67920 = 1.0;
        double r67921 = 9.0;
        double r67922 = r67920 / r67921;
        double r67923 = fma(r67919, r67920, r67922);
        double r67924 = 2.0;
        double r67925 = r67924 / r67921;
        double r67926 = r67923 * r67925;
        double r67927 = r67926 * r67920;
        return r67927;
}

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 2020014 +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))))