Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 386.0ms

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 r71251 = 2.0;
        double r71252 = 1.0;
        double r71253 = 9.0;
        double r71254 = r71252 / r71253;
        double r71255 = r71252 * r71254;
        double r71256 = r71254 * r71254;
        double r71257 = r71255 + r71256;
        double r71258 = r71254 * r71252;
        double r71259 = r71257 + r71258;
        double r71260 = r71251 * r71259;
        return r71260;
}

↓

double f() {
        double r71261 = 2.0;
        double r71262 = 1.0;
        double r71263 = 9.0;
        double r71264 = r71262 / r71263;
        double r71265 = fma(r71261, r71262, r71264);
        double r71266 = 2.0;
        double r71267 = r71266 / r71263;
        double r71268 = r71265 * r71267;
        double r71269 = r71268 * r71262;
        return r71269;
}

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 2020018 +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))))