Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 402.0ms

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 r77175 = 2.0;
        double r77176 = 1.0;
        double r77177 = 9.0;
        double r77178 = r77176 / r77177;
        double r77179 = r77176 * r77178;
        double r77180 = r77178 * r77178;
        double r77181 = r77179 + r77180;
        double r77182 = r77178 * r77176;
        double r77183 = r77181 + r77182;
        double r77184 = r77175 * r77183;
        return r77184;
}

↓

double f() {
        double r77185 = 2.0;
        double r77186 = 1.0;
        double r77187 = 9.0;
        double r77188 = r77186 / r77187;
        double r77189 = fma(r77185, r77186, r77188);
        double r77190 = 2.0;
        double r77191 = r77190 / r77187;
        double r77192 = r77189 * r77191;
        double r77193 = r77192 * r77186;
        return r77193;
}

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 2020001 +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))))