Average Error: 0 → 0
Time: 1.7s
Precision: 64
\[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]
↓
\[\frac{1}{9} \cdot \left(2 \cdot \mathsf{fma}\left(2, 1, \frac{1}{9}\right)\right)\]
2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)
↓
\frac{1}{9} \cdot \left(2 \cdot \mathsf{fma}\left(2, 1, \frac{1}{9}\right)\right)
double f() {
        double r124241 = 2.0;
        double r124242 = 1.0;
        double r124243 = 9.0;
        double r124244 = r124242 / r124243;
        double r124245 = r124242 * r124244;
        double r124246 = r124244 * r124244;
        double r124247 = r124245 + r124246;
        double r124248 = r124244 * r124242;
        double r124249 = r124247 + r124248;
        double r124250 = r124241 * r124249;
        return r124250;
}
↓
double f() {
        double r124251 = 1.0;
        double r124252 = 9.0;
        double r124253 = r124251 / r124252;
        double r124254 = 2.0;
        double r124255 = 2.0;
        double r124256 = fma(r124255, r124251, r124253);
        double r124257 = r124254 * r124256;
        double r124258 = r124253 * r124257;
        return r124258;
}

Error

Target

Original0
Target0
Herbie0
\[\left(\left(\frac{1}{9} \cdot 1\right) \cdot 2 + 2 \cdot \left(\frac{1}{9} \cdot \frac{1}{9}\right)\right) + 2 \cdot \left(1 \cdot \frac{1}{9}\right)\]

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. Simplified0

    \[\leadsto \color{blue}{\frac{1}{9} \cdot \left(2 \cdot \mathsf{fma}\left(2, 1, \frac{1}{9}\right)\right)}\]

  3. Final simplification0

    \[\leadsto \frac{1}{9} \cdot \left(2 \cdot \mathsf{fma}\left(2, 1, \frac{1}{9}\right)\right)\]

Reproduce

herbie shell --seed 2020045 +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))))