Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 774.0ms

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 r34772 = 2.0;
        double r34773 = 1.0;
        double r34774 = 9.0;
        double r34775 = r34773 / r34774;
        double r34776 = r34773 * r34775;
        double r34777 = r34775 * r34775;
        double r34778 = r34776 + r34777;
        double r34779 = r34775 * r34773;
        double r34780 = r34778 + r34779;
        double r34781 = r34772 * r34780;
        return r34781;
}

↓

double f() {
        double r34782 = 2.0;
        double r34783 = 1.0;
        double r34784 = 9.0;
        double r34785 = r34783 / r34784;
        double r34786 = fma(r34782, r34783, r34785);
        double r34787 = 2.0;
        double r34788 = r34787 / r34784;
        double r34789 = r34786 * r34788;
        double r34790 = r34789 * r34783;
        return r34790;
}

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 2020035 +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))))